EULERSEC[0] 1
[1] 0, 1
[2] -1, 0, 1
[3] 0, -3, 0, 1
[4] 5, 0, -6, 0, 1
[5] 0, 25, 0, -10, 0, 1

      OEIS Similars: A119879, A081658, A153641

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA1198791 0 1 -1 0 1 0 -3 0 1 5 0 -6 0 1 0 25 0 -10 0 1 -61 0 75 0 -15 0 1 0 -427 0 175 0 -21 0 1 1385 0
StdRevT(n, n - k), 0 ≤ k ≤ nA0816581 1 0 1 0 -1 1 0 -3 0 1 0 -6 0 5 1 0 -10 0 25 0 1 0 -15 0 75 0 -61 1 0 -21 0 175 0 -427 0 1 0 -28 0
StdInvT-1(n, k), 0 ≤ k ≤ nA1194671 0 1 1 0 1 0 3 0 1 1 0 6 0 1 0 5 0 10 0 1 1 0 15 0 15 0 1 0 7 0 35 0 21 0 1 1 0 28 0 70 0 28 0 1 0
StdRevInvT-1(n, n - k), 0 ≤ k ≤ nA1416651 1 0 1 0 1 1 0 3 0 1 0 6 0 1 1 0 10 0 5 0 1 0 15 0 15 0 1 1 0 21 0 35 0 7 0 1 0 28 0 70 0 28 0 1 1
StdAccsee docsmissing1 0 1 -1 -1 0 0 -3 -3 -2 5 5 -1 -1 0 0 25 25 15 15 16 -61 -61 14 14 -1 -1 0 0 -427 -427 -252 -252
StdAccRevsee docsmissing1 1 1 1 1 0 1 1 -2 -2 1 1 -5 -5 0 1 1 -9 -9 16 16 1 1 -14 -14 61 61 0 1 1 -20 -20 155 155 -272 -272
StdAntiDiagsee docsmissing1 0 -1 1 0 0 5 -3 1 0 0 0 -61 25 -6 1 0 0 0 0 1385 -427 75 -10 1 0 0 0 0 0 -50521 12465 -1708 175
StdDiffx1T(n, k) (k+1)missing1 0 2 -1 0 3 0 -6 0 4 5 0 -18 0 5 0 50 0 -40 0 6 -61 0 225 0 -75 0 7 0 -854 0 700 0 -126 0 8 1385 0
StdRowSum∑ k=0..n T(n, k)A0090061 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0
StdEvenSum∑ k=0..n T(n, k) even(k)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
StdOddSum∑ k=0..n T(n, k) odd(k)A0090060 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0
StdAltSum∑ k=0..n T(n, k) (-1)^kA0090061 -1 0 2 0 -16 0 272 0 -7936 0 353792 0 -22368256 0 1903757312 0 -209865342976 0 29088885112832 0
StdAbsSum∑ k=0..n | T(n, k) |A0037011 1 2 4 12 36 152 624 3472 18256 126752 814144 6781632 51475776 500231552 4381112064 48656756992
StdDiagSum∑ k=0..n // 2 T(n - k, k)missing1 0 0 0 3 0 -41 0 1024 0 -39603 0 2204565 0 -167343104 0 16633258447 0 -2097966372405 0
StdAccSum∑ k=0..n ∑ j=0..k T(n, j)missing1 1 -2 -8 8 96 -96 -2176 2176 79360 -79360 -4245504 4245504 313155584 -313155584 -30460116992
StdAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)A0097251 2 2 -2 -8 16 96 -272 -2176 7936 79360 -353792 -4245504 22368256 313155584 -1903757312
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 3 30 50 4575 32025 11827900 21290220 2689008011550 9859696042350 31978129648682517300
StdRowGcdGcd k=0..n | T(n, k) | > 1A1554571 1 1 3 1 5 1 7 1 3 1 11 1 13 1 1 1 17 1 19 1 1 1 23 1 5 1 3 1 29 1 31 1 1 1 1 1 37 1 1 1 41 1 43 1
StdRowMaxMax k=0..n | T(n, k) |missing1 1 1 3 6 25 75 427 1708 12465 62325 555731 3334386 35135945 245951615 2990414715 23923317720
StdColMiddleT(n, n // 2)missing1 0 0 -3 -6 0 0 175 350 0 0 -28182 -56364 0 0 8912475 17824950 0 0 -4667028938 -9334057876 0 0
StdCentralET(2 n, n)A2144451 0 -6 0 350 0 -56364 0 17824950 0 -9334057876 0 7308698191340 0 -7997684730384600 0
StdCentralOT(2 n + 1, n)missing0 -3 0 175 0 -28182 0 8912475 0 -4667028938 0 3654349095670 0 -3998842365192300 0
StdColLeftT(n, 0)A1220451 0 -1 0 5 0 -61 0 1385 0 -50521 0 2702765 0 -199360981 0 19391512145 0 -2404879675441 0
StdColRightT(n, n)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdBinConv∑ k=0..n C(n, k) T(n, k)missing1 1 0 -8 -30 26 840 2696 -22722 -240146 282480 19114976 71133348 -1558651340 -16495010896
StdInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 1 0 -8 -30 26 840 2696 -22722 -240146 282480 19114976 71133348 -1558651340 -16495010896
StdTransNat0∑ k=0..n T(n, k) kA1095730 1 2 0 -8 0 96 0 -2176 0 79360 0 -4245504 0 313155584 0 -30460116992 0 3777576173568 0
StdTransNat1∑ k=0..n T(n, k) (k + 1)A0097251 2 2 -2 -8 16 96 -272 -2176 7936 79360 -353792 -4245504 22368256 313155584 -1903757312
StdTransSqrs∑ k=0..n T(n, k) k^2missing0 1 4 6 -8 -40 96 672 -2176 -19584 79360 872960 -4245504 -55191552 313155584 4697333760
StdPosHalf∑ k=0..n 2^n T(n, k) (1/2)^kA0015861 1 -3 -11 57 361 -2763 -24611 250737 2873041 -36581523 -512343611 7828053417 129570724921
StdNegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^kA0015861 1 -3 -11 57 361 -2763 -24611 250737 2873041 -36581523 -512343611 7828053417 129570724921
StdDiagRow2T(n + 2, n)A000217-1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 -276
StdDiagCol1T(n + 1, 1)A0098431 0 -3 0 25 0 -427 0 12465 0 -555731 0 35135945 0 -2990414715 0 329655706465 0 -45692713833379 0
StdDiagCol2T(n + 2, 2)missing1 0 -6 0 75 0 -1708 0 62325 0 -3334386 0 245951615 0 -23923317720 0 2966901358185 0
StdDiagCol3T(n + 3, 3)missing1 0 -10 0 175 0 -5124 0 228525 0 -14449006 0 1229758075 0 -135565467080 0 18790375268505 0
StdPolysee docsA2474981 0 1 -1 1 1 0 0 2 1 5 -2 3 3 1 0 0 2 8 4 1 -61 16 -3 18 15 5 1 0 0 2 32 52 24 6 1 1385 -272 63 48
StdPolyRow1∑ k=0..1 T(1, k) n^kA0000270 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
StdPolyRow2∑ k=0..2 T(2, k) n^kA005563-1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728
StdPolyRow3∑ k=0..3 T(3, k) n^kA0587940 -2 2 18 52 110 198 322 488 702 970 1298 1692 2158 2702 3330 4048 4862 5778 6802 7940 9198 10582
StdPolyCol2∑ k=0..n T(n, k) 2^kA1198801 2 3 2 -3 2 63 2 -1383 2 50523 2 -2702763 2 199360983 2 -19391512143 2 2404879675443 2
StdPolyCol3∑ k=0..n T(n, k) 3^kA1198811 3 8 18 32 48 128 528 512 -6912 2048 357888 8192 -22351872 32768 1903822848 131072 -209865080832
StdPolyDiag∑ k=0..n T(n, k) n^kA3025851 1 3 18 165 2000 29855 527632 10762857 248811264 6428081979 183537694208 5739195739277
AltTriangleT(n, k), 0 ≤ k ≤ nA1198791 0 -1 -1 0 1 0 3 0 -1 5 0 -6 0 1 0 -25 0 10 0 -1 -61 0 75 0 -15 0 1 0 427 0 -175 0 21 0 -1 1385 0
AltRevT(n, n - k), 0 ≤ k ≤ nA0816581 -1 0 1 0 -1 -1 0 3 0 1 0 -6 0 5 -1 0 10 0 -25 0 1 0 -15 0 75 0 -61 -1 0 21 0 -175 0 427 0 1 0 -28
AltInvT-1(n, k), 0 ≤ k ≤ nmissing1 0 1 1 0 1 0 -3 0 1 1 0 6 0 1 0 55 0 -10 0 1 1 0 15 0 15 0 1 0 -2107 0 385 0 -21 0 1 1 0 28 0 70 0
AltRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 0 1 1 0 -3 0 1 0 6 0 1 1 0 -10 0 55 0 1 0 15 0 15 0 1 1 0 -21 0 385 0 -2107 0 1 0 28 0 70 0
AltAccsee docsmissing1 0 -1 -1 -1 0 0 3 3 2 5 5 -1 -1 0 0 -25 -25 -15 -15 -16 -61 -61 14 14 -1 -1 0 0 427 427 252 252
AltAccRevsee docsmissing1 -1 -1 1 1 0 -1 -1 2 2 1 1 -5 -5 0 -1 -1 9 9 -16 -16 1 1 -14 -14 61 61 0 -1 -1 20 20 -155 -155 272
AltAntiDiagsee docsmissing1 0 -1 -1 0 0 5 3 1 0 0 0 -61 -25 -6 -1 0 0 0 0 1385 427 75 10 1 0 0 0 0 0 -50521 -12465 -1708 -175
AltDiffx1T(n, k) (k+1)missing1 0 -2 -1 0 3 0 6 0 -4 5 0 -18 0 5 0 -50 0 40 0 -6 -61 0 225 0 -75 0 7 0 854 0 -700 0 126 0 -8 1385
AltRowSum∑ k=0..n T(n, k)A0090061 -1 0 2 0 -16 0 272 0 -7936 0 353792 0 -22368256 0 1903757312 0 -209865342976 0 29088885112832 0
AltEvenSum∑ k=0..n T(n, k) even(k)A0000071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
AltOddSum∑ k=0..n T(n, k) odd(k)A0090060 -1 0 2 0 -16 0 272 0 -7936 0 353792 0 -22368256 0 1903757312 0 -209865342976 0 29088885112832 0
AltAltSum∑ k=0..n T(n, k) (-1)^kA0090061 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0
AltAbsSum∑ k=0..n | T(n, k) |A0037011 1 2 4 12 36 152 624 3472 18256 126752 814144 6781632 51475776 500231552 4381112064 48656756992
AltDiagSum∑ k=0..n // 2 T(n - k, k)missing1 0 -2 0 9 0 -93 0 1898 0 -64885 0 3326317 0 -238073306 0 22643042325 0 -2759740869777 0
AltAccSum∑ k=0..n ∑ j=0..k T(n, j)missing1 -1 -2 8 8 -96 -96 2176 2176 -79360 -79360 4245504 4245504 -313155584 -313155584 30460116992
AltAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)A0097251 -2 2 2 -8 -16 96 272 -2176 -7936 79360 353792 -4245504 -22368256 313155584 1903757312
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 3 30 50 4575 32025 11827900 21290220 2689008011550 9859696042350 31978129648682517300
AltRowGcdGcd k=0..n | T(n, k) | > 1A1554571 1 1 3 1 5 1 7 1 3 1 11 1 13 1 1 1 17 1 19 1 1 1 23 1 5 1 3 1 29 1 31 1 1 1 1 1 37 1 1 1 41 1 43 1
AltRowMaxMax k=0..n | T(n, k) |missing1 1 1 3 6 25 75 427 1708 12465 62325 555731 3334386 35135945 245951615 2990414715 23923317720
AltColMiddleT(n, n // 2)missing1 0 0 3 -6 0 0 -175 350 0 0 28182 -56364 0 0 -8912475 17824950 0 0 4667028938 -9334057876 0 0
AltCentralET(2 n, n)A2144451 0 -6 0 350 0 -56364 0 17824950 0 -9334057876 0 7308698191340 0 -7997684730384600 0
AltCentralOT(2 n + 1, n)missing0 3 0 -175 0 28182 0 -8912475 0 4667028938 0 -3654349095670 0 3998842365192300 0
AltColLeftT(n, 0)A1220451 0 -1 0 5 0 -61 0 1385 0 -50521 0 2702765 0 -199360981 0 19391512145 0 -2404879675441 0
AltBinConv∑ k=0..n C(n, k) T(n, k)missing1 -1 0 8 -30 -26 840 -2696 -22722 240146 282480 -19114976 71133348 1558651340 -16495010896
AltInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 0 8 -30 -26 840 -2696 -22722 240146 282480 -19114976 71133348 1558651340 -16495010896
AltTransNat0∑ k=0..n T(n, k) kA1095730 -1 2 0 -8 0 96 0 -2176 0 79360 0 -4245504 0 313155584 0 -30460116992 0 3777576173568 0
AltTransNat1∑ k=0..n T(n, k) (k + 1)A0097251 -2 2 2 -8 -16 96 272 -2176 -7936 79360 353792 -4245504 -22368256 313155584 1903757312
AltTransSqrs∑ k=0..n T(n, k) k^2missing0 -1 4 -6 -8 40 96 -672 -2176 19584 79360 -872960 -4245504 55191552 313155584 -4697333760
AltPosHalf∑ k=0..n 2^n T(n, k) (1/2)^kA0015861 -1 -3 11 57 -361 -2763 24611 250737 -2873041 -36581523 512343611 7828053417 -129570724921
AltNegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^kA0015861 -1 -3 11 57 -361 -2763 24611 250737 -2873041 -36581523 512343611 7828053417 -129570724921
AltDiagRow2T(n + 2, n)A000217-1 3 -6 10 -15 21 -28 36 -45 55 -66 78 -91 105 -120 136 -153 171 -190 210 -231 253 -276 300 -325
AltDiagCol1T(n + 1, 1)A009843-1 0 3 0 -25 0 427 0 -12465 0 555731 0 -35135945 0 2990414715 0 -329655706465 0 45692713833379 0
AltDiagCol2T(n + 2, 2)missing1 0 -6 0 75 0 -1708 0 62325 0 -3334386 0 245951615 0 -23923317720 0 2966901358185 0
AltDiagCol3T(n + 3, 3)missing-1 0 10 0 -175 0 5124 0 -228525 0 14449006 0 -1229758075 0 135565467080 0 -18790375268505 0
AltPolysee docsA2474981 0 1 -1 -1 1 0 0 -2 1 5 2 3 -3 1 0 0 -2 8 -4 1 -61 -16 -3 -18 15 -5 1 0 0 -2 32 -52 24 -6 1 1385
AltPolyRow1∑ k=0..1 T(1, k) n^kA0000270 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26
AltPolyRow2∑ k=0..2 T(2, k) n^kA005563-1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728
AltPolyRow3∑ k=0..3 T(3, k) n^kA0587940 2 -2 -18 -52 -110 -198 -322 -488 -702 -970 -1298 -1692 -2158 -2702 -3330 -4048 -4862 -5778 -6802
AltPolyCol2∑ k=0..n T(n, k) 2^kA1198801 -2 3 -2 -3 -2 63 -2 -1383 -2 50523 -2 -2702763 -2 199360983 -2 -19391512143 -2 2404879675443 -2
AltPolyCol3∑ k=0..n T(n, k) 3^kA1198811 -3 8 -18 32 -48 128 -528 512 6912 2048 -357888 8192 22351872 32768 -1903822848 131072
AltPolyDiag∑ k=0..n T(n, k) n^kA3025851 -1 3 -18 165 -2000 29855 -527632 10762857 -248811264 6428081979 -183537694208 5739195739277
RevTriangleT(n, k), 0 ≤ k ≤ nA0816581 1 0 1 0 -1 1 0 -3 0 1 0 -6 0 5 1 0 -10 0 25 0 1 0 -15 0 75 0 -61 1 0 -21 0 175 0 -427 0 1 0 -28 0
RevInvRev(T(n, n - k))-1, 0 ≤ k ≤ nA1194671 0 1 1 0 1 0 3 0 1 1 0 6 0 1 0 5 0 10 0 1 1 0 15 0 15 0 1 0 7 0 35 0 21 0 1 1 0 28 0 70 0 28 0 1 0
RevAccsee docsmissing1 1 1 1 1 0 1 1 -2 -2 1 1 -5 -5 0 1 1 -9 -9 16 16 1 1 -14 -14 61 61 0 1 1 -20 -20 155 155 -272 -272
RevAccRevsee docsmissing1 0 1 -1 -1 0 0 -3 -3 -2 5 5 -1 -1 0 0 25 25 15 15 16 -61 -61 14 14 -1 -1 0 0 -427 -427 -252 -252
RevAntiDiagsee docsmissing1 1 1 0 1 0 1 0 -1 1 0 -3 1 0 -6 0 1 0 -10 0 1 0 -15 0 5 1 0 -21 0 25 1 0 -28 0 75 0 1 0 -36 0 175
RevDiffx1T(n, k) (k+1)missing1 1 0 1 0 -3 1 0 -9 0 1 0 -18 0 25 1 0 -30 0 125 0 1 0 -45 0 375 0 -427 1 0 -63 0 875 0 -2989 0 1 0
RevRowSum∑ k=0..n T(n, k)A0090061 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0
RevEvenSum∑ k=0..n T(n, k) even(k)A0090061 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0
RevAltSum∑ k=0..n T(n, k) (-1)^kA0090061 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0
RevAbsSum∑ k=0..n | T(n, k) |A0037011 1 2 4 12 36 152 624 3472 18256 126752 814144 6781632 51475776 500231552 4381112064 48656756992
RevDiagSum∑ k=0..n // 2 T(n - k, k)missing1 1 1 1 0 -2 -5 -9 -9 5 48 140 245 149 -723 -3551 -9040 -12246 10847 130539 460819 933189 351392
RevAccSum∑ k=0..n ∑ j=0..k T(n, j)A0097251 2 2 -2 -8 16 96 -272 -2176 7936 79360 -353792 -4245504 22368256 313155584 -1903757312
RevAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)missing1 1 -2 -8 8 96 -96 -2176 2176 79360 -79360 -4245504 4245504 313155584 -313155584 -30460116992
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 3 30 50 4575 32025 11827900 21290220 2689008011550 9859696042350 31978129648682517300
RevRowGcdGcd k=0..n | T(n, k) | > 1A1554571 1 1 3 1 5 1 7 1 3 1 11 1 13 1 1 1 17 1 19 1 1 1 23 1 5 1 3 1 29 1 31 1 1 1 1 1 37 1 1 1 41 1 43 1
RevRowMaxMax k=0..n | T(n, k) |missing1 1 1 3 6 25 75 427 1708 12465 62325 555731 3334386 35135945 245951615 2990414715 23923317720
RevColMiddleT(n, n // 2)missing1 1 0 0 -6 -10 0 0 350 630 0 0 -56364 -104676 0 0 17824950 33669350 0 0 -9334057876 -17819565036 0
RevCentralET(2 n, n)A2144451 0 -6 0 350 0 -56364 0 17824950 0 -9334057876 0 7308698191340 0 -7997684730384600 0
RevCentralOT(2 n + 1, n)missing1 0 -10 0 630 0 -104676 0 33669350 0 -17819565036 0 14055188829500 0 -15462190478743560 0
RevColLeftT(n, 0)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
RevColRightT(n, n)A1220451 0 -1 0 5 0 -61 0 1385 0 -50521 0 2702765 0 -199360981 0 19391512145 0 -2404879675441 0
RevBinConv∑ k=0..n C(n, k) T(n, k)missing1 1 0 -8 -30 26 840 2696 -22722 -240146 282480 19114976 71133348 -1558651340 -16495010896
RevInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 0 8 -30 -26 840 -2696 -22722 240146 282480 -19114976 71133348 1558651340 -16495010896
RevTransNat0∑ k=0..n T(n, k) kmissing0 0 -2 -6 8 80 -96 -1904 2176 71424 -79360 -3891712 4245504 290787328 -313155584 -28556359680
RevTransNat1∑ k=0..n T(n, k) (k + 1)missing1 1 -2 -8 8 96 -96 -2176 2176 79360 -79360 -4245504 4245504 313155584 -313155584 -30460116992
RevTransSqrs∑ k=0..n T(n, k) k^2missing0 0 -4 -12 56 360 -1056 -12656 32640 623232 -1507840 -41935872 97646592 3725043712 -8455200768
RevPosHalf∑ k=0..n 2^n T(n, k) (1/2)^kA1198801 2 3 2 -3 2 63 2 -1383 2 50523 2 -2702763 2 199360983 2 -19391512143 2 2404879675443 2
RevNegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^kA1198801 -2 3 -2 -3 -2 63 -2 -1383 -2 50523 -2 -2702763 -2 199360983 -2 -19391512143 -2 2404879675443 -2
RevDiagRow1T(n + 1, n)A0098431 0 -3 0 25 0 -427 0 12465 0 -555731 0 35135945 0 -2990414715 0 329655706465 0 -45692713833379 0
RevDiagRow2T(n + 2, n)missing1 0 -6 0 75 0 -1708 0 62325 0 -3334386 0 245951615 0 -23923317720 0 2966901358185 0
RevDiagRow3T(n + 3, n)missing1 0 -10 0 175 0 -5124 0 228525 0 -14449006 0 1229758075 0 -135565467080 0 18790375268505 0
RevDiagCol2T(n + 2, 2)A000217-1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 -276
RevPolysee docsmissing1 1 1 1 1 1 1 0 1 1 1 -2 -3 1 1 1 0 -11 -8 1 1 1 16 57 -26 -15 1 1 1 0 361 352 -47 -24 1 1 1 -272
RevPolyRow1∑ k=0..1 T(1, k) n^kA0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
RevPolyRow2∑ k=0..2 T(2, k) n^kA0055631 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483
RevPolyRow3∑ k=0..3 T(3, k) n^kA0806631 -2 -11 -26 -47 -74 -107 -146 -191 -242 -299 -362 -431 -506 -587 -674 -767 -866 -971 -1082 -1199
RevPolyCol2∑ k=0..n T(n, k) 2^kA0015861 1 -3 -11 57 361 -2763 -24611 250737 2873041 -36581523 -512343611 7828053417 129570724921
RevPolyCol3∑ k=0..n T(n, k) 3^kA0008101 1 -8 -26 352 1936 -38528 -297296 7869952 78098176 -2583554048 -31336418816 1243925143552
RevPolyDiag∑ k=0..n T(n, k) n^kA3780631 1 -3 -26 1185 15376 -2749355 -49816976 22790134017 533858404096 -498990299504499
InvTriangleT(n, k), 0 ≤ k ≤ nA1194671 0 1 1 0 1 0 3 0 1 1 0 6 0 1 0 5 0 10 0 1 1 0 15 0 15 0 1 0 7 0 35 0 21 0 1 1 0 28 0 70 0 28 0 1 0
InvRevT(n, n - k), 0 ≤ k ≤ nA1416651 1 0 1 0 1 1 0 3 0 1 0 6 0 1 1 0 10 0 5 0 1 0 15 0 15 0 1 1 0 21 0 35 0 7 0 1 0 28 0 70 0 28 0 1 1
InvRevInvT-1(n, n - k), 0 ≤ k ≤ nA0816581 1 0 1 0 -1 1 0 -3 0 1 0 -6 0 5 1 0 -10 0 25 0 1 0 -15 0 75 0 -61 1 0 -21 0 175 0 -427 0 1 0 -28 0
InvAccsee docsmissing1 0 1 1 1 2 0 3 3 4 1 1 7 7 8 0 5 5 15 15 16 1 1 16 16 31 31 32 0 7 7 42 42 63 63 64 1 1 29 29 99
InvAccRevsee docsmissing1 1 1 1 1 2 1 1 4 4 1 1 7 7 8 1 1 11 11 16 16 1 1 16 16 31 31 32 1 1 22 22 57 57 64 64 1 1 29 29 99
InvAntiDiagsee docsmissing1 0 1 1 0 0 1 3 1 0 0 0 1 5 6 1 0 0 0 0 1 7 15 10 1 0 0 0 0 0 1 9 28 35 15 1 0 0 0 0 0 0 1 11 45 84
InvDiffx1T(n, k) (k+1)missing1 0 2 1 0 3 0 6 0 4 1 0 18 0 5 0 10 0 40 0 6 1 0 45 0 75 0 7 0 14 0 140 0 126 0 8 1 0 84 0 350 0
InvRowSum∑ k=0..n T(n, k)A0000791 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
InvEvenSum∑ k=0..n T(n, k) even(k)A1034241 0 2 0 8 0 32 0 128 0 512 0 2048 0 8192 0 32768 0 131072 0 524288 0 2097152 0 8388608 0 33554432 0
InvOddSum∑ k=0..n T(n, k) odd(k)A1995720 1 0 4 0 16 0 64 0 256 0 1024 0 4096 0 16384 0 65536 0 262144 0 1048576 0 4194304 0 16777216 0
InvAltSum∑ k=0..n T(n, k) (-1)^kA0000791 -1 2 -4 8 -16 32 -64 128 -256 512 -1024 2048 -4096 8192 -16384 32768 -65536 131072 -262144 524288
InvAbsSum∑ k=0..n | T(n, k) |A0000791 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
InvDiagSum∑ k=0..n // 2 T(n - k, k)A0015191 0 2 0 5 0 13 0 34 0 89 0 233 0 610 0 1597 0 4181 0 10946 0 28657 0 75025 0 196418 0 514229 0
InvAccSum∑ k=0..n ∑ j=0..k T(n, j)A0874471 1 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264 294912 622592 1310720 2752512
InvAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)A0874471 2 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264 294912 622592 1310720 2752512
InvRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 3 6 10 15 105 140 252 630 2310 13860 25740 3003 45045 360360 680680 3063060 11639628 5542680
InvRowGcdGcd k=0..n | T(n, k) | > 1missing1 1 1 3 6 5 15 7 14 3 15 11 33 13 91 1 2 17 51 19 19 1 11 23 23 5 65 3 3 29 435 31 62 1 17 1 3 37
InvRowMaxMax k=0..n | T(n, k) |A2142821 1 1 3 6 10 15 35 70 126 210 462 924 1716 3003 6435 12870 24310 43758 92378 184756 352716 646646
InvColMiddleT(n, n // 2)missing1 0 0 3 6 0 0 35 70 0 0 462 924 0 0 6435 12870 0 0 92378 184756 0 0 1352078 2704156 0 0 20058300
InvCentralET(2 n, n)A0014481 0 6 0 70 0 924 0 12870 0 184756 0 2704156 0 40116600 0 601080390 0 9075135300 0 137846528820 0
InvCentralOT(2 n + 1, n)A1000330 3 0 35 0 462 0 6435 0 92378 0 1352078 0 20058300 0 300540195 0 4537567650 0 68923264410 0
InvColLeftT(n, 0)A0000351 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
InvColRightT(n, n)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
InvBinConv∑ k=0..n C(n, k) T(n, k)A1193581 1 2 10 38 126 452 1716 6470 24310 92252 352716 1352540 5200300 20056584 77558760 300546630
InvInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kA1193581 1 2 10 38 126 452 1716 6470 24310 92252 352716 1352540 5200300 20056584 77558760 300546630
InvTransNat0∑ k=0..n T(n, k) kA0577110 1 2 6 16 40 96 224 512 1152 2560 5632 12288 26624 57344 122880 262144 557056 1179648 2490368
InvTransNat1∑ k=0..n T(n, k) (k + 1)A0874471 2 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264 294912 622592 1310720 2752512
InvTransSqrs∑ k=0..n T(n, k) k^2A0809290 1 4 12 40 120 336 896 2304 5760 14080 33792 79872 186368 430080 983040 2228224 5013504 11206656
InvPosHalf∑ k=0..n 2^n T(n, k) (1/2)^kA0467171 1 5 13 41 121 365 1093 3281 9841 29525 88573 265721 797161 2391485 7174453 21523361 64570081
InvNegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^kA0467171 1 5 13 41 121 365 1093 3281 9841 29525 88573 265721 797161 2391485 7174453 21523361 64570081
InvDiagRow2T(n + 2, n)A0002171 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435
InvDiagCol1T(n + 1, 1)A1933561 0 3 0 5 0 7 0 9 0 11 0 13 0 15 0 17 0 19 0 21 0 23 0 25 0 27 0 29 0 31 0 33 0 35 0 37 0 39 0 41 0
InvDiagCol2T(n + 2, 2)A0003841 0 6 0 15 0 28 0 45 0 66 0 91 0 120 0 153 0 190 0 231 0 276 0 325 0 378 0 435 0 496 0 561 0 630 0
InvDiagCol3T(n + 3, 3)A0004471 0 10 0 35 0 84 0 165 0 286 0 455 0 680 0 969 0 1330 0 1771 0 2300 0 2925 0 3654 0 4495 0 5456 0
InvPolysee docsmissing1 0 1 1 1 1 0 2 2 1 1 4 5 3 1 0 8 14 10 4 1 1 16 41 36 17 5 1 0 32 122 136 76 26 6 1 1 64 365 528
InvPolyRow1∑ k=0..1 T(1, k) n^kA0000270 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
InvPolyRow2∑ k=0..2 T(2, k) n^kA0025221 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730
InvPolyRow3∑ k=0..3 T(3, k) n^kA0799080 4 14 36 76 140 234 364 536 756 1030 1364 1764 2236 2786 3420 4144 4964 5886 6916 8060 9324 10714
InvPolyCol2∑ k=0..n T(n, k) 2^kA0070511 2 5 14 41 122 365 1094 3281 9842 29525 88574 265721 797162 2391485 7174454 21523361 64570082
InvPolyCol3∑ k=0..n T(n, k) 3^kA0075821 3 10 36 136 528 2080 8256 32896 131328 524800 2098176 8390656 33558528 134225920 536887296
InvPolyDiag∑ k=0..n T(n, k) n^kA0620241 1 5 36 353 4400 66637 1188544 24405761 567108864 14712104501 421504185344 13218256749601
Inv:RevTriangleT(n, k), 0 ≤ k ≤ nA1416651 1 0 1 0 1 1 0 3 0 1 0 6 0 1 1 0 10 0 5 0 1 0 15 0 15 0 1 1 0 21 0 35 0 7 0 1 0 28 0 70 0 28 0 1 1
Inv:RevRevT(n, n - k), 0 ≤ k ≤ nA1194671 0 1 1 0 1 0 3 0 1 1 0 6 0 1 0 5 0 10 0 1 1 0 15 0 15 0 1 0 7 0 35 0 21 0 1 1 0 28 0 70 0 28 0 1 0
Inv:RevInvRev(T(n, n - k))-1, 0 ≤ k ≤ nA1198791 0 1 -1 0 1 0 -3 0 1 5 0 -6 0 1 0 25 0 -10 0 1 -61 0 75 0 -15 0 1 0 -427 0 175 0 -21 0 1 1385 0
Inv:RevAccsee docsmissing1 1 1 1 1 2 1 1 4 4 1 1 7 7 8 1 1 11 11 16 16 1 1 16 16 31 31 32 1 1 22 22 57 57 64 64 1 1 29 29 99
Inv:RevAccRevsee docsmissing1 0 1 1 1 2 0 3 3 4 1 1 7 7 8 0 5 5 15 15 16 1 1 16 16 31 31 32 0 7 7 42 42 63 63 64 1 1 29 29 99
Inv:RevAntiDiagsee docsmissing1 1 1 0 1 0 1 0 1 1 0 3 1 0 6 0 1 0 10 0 1 0 15 0 1 1 0 21 0 5 1 0 28 0 15 0 1 0 36 0 35 0 1 0 45 0
Inv:RevDiffx1T(n, k) (k+1)missing1 1 0 1 0 3 1 0 9 0 1 0 18 0 5 1 0 30 0 25 0 1 0 45 0 75 0 7 1 0 63 0 175 0 49 0 1 0 84 0 350 0 196
Inv:RevRowSum∑ k=0..n T(n, k)A0000791 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
Inv:RevEvenSum∑ k=0..n T(n, k) even(k)A0000791 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
Inv:RevAltSum∑ k=0..n T(n, k) (-1)^kA0000791 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
Inv:RevAbsSum∑ k=0..n | T(n, k) |A0000791 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
Inv:RevDiagSum∑ k=0..n // 2 T(n - k, k)A0052521 1 1 1 2 4 7 11 17 27 44 72 117 189 305 493 798 1292 2091 3383 5473 8855 14328 23184 37513 60697
Inv:RevAccSum∑ k=0..n ∑ j=0..k T(n, j)A0874471 2 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264 294912 622592 1310720 2752512
Inv:RevAccRevSum∑ k=0..n ∑ j=0..k T(n, n - j)A0874471 1 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264 294912 622592 1310720 2752512
Inv:RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 3 6 10 15 105 140 252 630 2310 13860 25740 3003 45045 360360 680680 3063060 11639628 5542680
Inv:RevRowGcdGcd k=0..n | T(n, k) | > 1missing1 1 1 3 6 5 15 7 14 3 15 11 33 13 91 1 2 17 51 19 19 1 11 23 23 5 65 3 3 29 435 31 62 1 17 1 3 37
Inv:RevRowMaxMax k=0..n | T(n, k) |A2142821 1 1 3 6 10 15 35 70 126 210 462 924 1716 3003 6435 12870 24310 43758 92378 184756 352716 646646
Inv:RevColMiddleT(n, n // 2)missing1 1 0 0 6 10 0 0 70 126 0 0 924 1716 0 0 12870 24310 0 0 184756 352716 0 0 2704156 5200300 0 0
Inv:RevCentralET(2 n, n)A0014481 0 6 0 70 0 924 0 12870 0 184756 0 2704156 0 40116600 0 601080390 0 9075135300 0 137846528820 0
Inv:RevCentralOT(2 n + 1, n)A0024581 0 10 0 126 0 1716 0 24310 0 352716 0 5200300 0 77558760 0 1166803110 0 17672631900 0 269128937220
Inv:RevColLeftT(n, 0)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Inv:RevColRightT(n, n)A0000351 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
Inv:RevBinConv∑ k=0..n C(n, k) T(n, k)A1193581 1 2 10 38 126 452 1716 6470 24310 92252 352716 1352540 5200300 20056584 77558760 300546630
Inv:RevInvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^kA1193581 -1 2 -10 38 -126 452 -1716 6470 -24310 92252 -352716 1352540 -5200300 20056584 -77558760
Inv:RevTransNat0∑ k=0..n T(n, k) kA0577110 0 2 6 16 40 96 224 512 1152 2560 5632 12288 26624 57344 122880 262144 557056 1179648 2490368
Inv:RevTransNat1∑ k=0..n T(n, k) (k + 1)A0874471 1 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264 294912 622592 1310720 2752512
Inv:RevTransSqrs∑ k=0..n T(n, k) k^2A0809290 0 4 12 40 120 336 896 2304 5760 14080 33792 79872 186368 430080 983040 2228224 5013504 11206656
Inv:RevPosHalf∑ k=0..n 2^n T(n, k) (1/2)^kA0070511 2 5 14 41 122 365 1094 3281 9842 29525 88574 265721 797162 2391485 7174454 21523361 64570082
Inv:RevNegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^kA0070511 -2 5 -14 41 -122 365 -1094 3281 -9842 29525 -88574 265721 -797162 2391485 -7174454 21523361
Inv:RevDiagRow1T(n + 1, n)A1933561 0 3 0 5 0 7 0 9 0 11 0 13 0 15 0 17 0 19 0 21 0 23 0 25 0 27 0 29 0 31 0 33 0 35 0 37 0 39 0 41 0
Inv:RevDiagRow2T(n + 2, n)A0003841 0 6 0 15 0 28 0 45 0 66 0 91 0 120 0 153 0 190 0 231 0 276 0 325 0 378 0 435 0 496 0 561 0 630 0
Inv:RevDiagRow3T(n + 3, n)A0004471 0 10 0 35 0 84 0 165 0 286 0 455 0 680 0 969 0 1330 0 1771 0 2300 0 2925 0 3654 0 4495 0 5456 0
Inv:RevDiagCol2T(n + 2, 2)A0002171 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435
Inv:RevPolysee docsmissing1 1 1 1 1 1 1 2 1 1 1 4 5 1 1 1 8 13 10 1 1 1 16 41 28 17 1 1 1 32 121 136 49 26 1 1 1 64 365 496
Inv:RevPolyRow1∑ k=0..1 T(1, k) n^kA0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Inv:RevPolyRow2∑ k=0..2 T(2, k) n^kA0025221 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730
Inv:RevPolyRow3∑ k=0..3 T(3, k) n^kA0561071 4 13 28 49 76 109 148 193 244 301 364 433 508 589 676 769 868 973 1084 1201 1324 1453 1588 1729
Inv:RevPolyCol2∑ k=0..n T(n, k) 2^kA0467171 1 5 13 41 121 365 1093 3281 9841 29525 88573 265721 797161 2391485 7174453 21523361 64570081
Inv:RevPolyCol3∑ k=0..n T(n, k) 3^kA0036651 1 10 28 136 496 2080 8128 32896 130816 524800 2096128 8390656 33550336 134225920 536854528
Inv:RevPolyDiag∑ k=0..n T(n, k) n^kA3456321 1 5 28 353 3376 66637 908608 24405761 432891136 14712104501 321504185344 13218256749601
 << TableSourceSimilarsIndex >> 

Note: The A-numbers are based on a finite number of numerical comparisons. They ignore the sign and the OEIS-offset. Sometimes they differ in the first few values. In such cases, we consider our version to be the better one because it has a common formula as a root. Since the offset of all triangles is 0 also the offset of all sequences is 0.