A350258
Triangle read by rows. T(n, k) = k! * BellPolynomial(n, k).
Original entry on oeis.org
1, 0, 1, 0, 2, 12, 0, 5, 44, 342, 0, 15, 188, 1854, 18144, 0, 52, 908, 11196, 130272, 1545600, 0, 203, 4860, 74106, 1016544, 13818600, 193030560, 0, 877, 28428, 531378, 8535264, 132204600, 2065854240, 33232948560
Offset: 0
Triangle starts:
[0] 1
[1] 0, 1
[2] 0, 2, 12
[3] 0, 5, 44, 342
[4] 0, 15, 188, 1854, 18144
[5] 0, 52, 908, 11196, 130272, 1545600
[6] 0, 203, 4860, 74106, 1016544, 13818600, 193030560
[7] 0, 877, 28428, 531378, 8535264, 132204600, 2065854240, 33232948560
-
A350258 := (n, k) -> ifelse(n = 0, 1, k! * BellB(n, k)):
seq(seq(A350258(n, k), k = 0..n), n = 0..7);
-
T[n_, k_] := k! BellB[n, k]; Table[T[n, k], {n, 0, 7}, {k, 0, n}] // Flatten
A350259
Triangle read by rows. T(n, k) = n! * BellPolynomial(n, k).
Original entry on oeis.org
1, 0, 1, 0, 4, 12, 0, 30, 132, 342, 0, 360, 2256, 7416, 18144, 0, 6240, 54480, 223920, 651360, 1545600, 0, 146160, 1749600, 8892720, 30496320, 82911600, 193030560, 0, 4420080, 71638560, 446357520, 1792405440, 5552593200, 14460979680, 33232948560
Offset: 0
Triangle starts:
[0] 1
[1] 0, 1
[2] 0, 4, 12
[3] 0, 30, 132, 342
[4] 0, 360, 2256, 7416, 18144
[5] 0, 6240, 54480, 223920, 651360, 1545600
[6] 0, 146160, 1749600, 8892720, 30496320, 82911600, 193030560
-
A350259 := (n, k) -> ifelse(n = 0, 1, n! * BellB(n, k)):
seq(seq(A350259(n, k), k = 0..n), n = 0..7);
-
T[n_, k_] := n! BellB[n, k]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
A350260
Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, 1/k) for k > 0, if k = 0 then T(n, k) = k^n.
Original entry on oeis.org
1, 0, 1, 0, 2, 3, 0, 5, 11, 19, 0, 15, 49, 109, 201, 0, 52, 257, 742, 1657, 3176, 0, 203, 1539, 5815, 15821, 35451, 69823, 0, 877, 10299, 51193, 170389, 447981, 1007407, 2026249, 0, 4140, 75905, 498118, 2032785, 6282416, 16157905, 36458010, 74565473
Offset: 0
Triangle starts:
[0] 1
[1] 0, 1
[2] 0, 2, 3
[3] 0, 5, 11, 19
[4] 0, 15, 49, 109, 201
[5] 0, 52, 257, 742, 1657, 3176
[6] 0, 203, 1539, 5815, 15821, 35451, 69823
[7] 0, 877, 10299, 51193, 170389, 447981, 1007407, 2026249
[8] 0, 4140, 75905, 498118, 2032785, 6282416, 16157905, 36458010, 74565473
-
A350260 := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, 1/k)):
seq(seq(A350260(n, k), k = 0..n), n = 0..8);
-
T[n_, k_] := If[k == 0, k^n, k^n BellB[n, 1/k]];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
A350261
Triangle read by rows. T(n, k) = k^n * BellPolynomial(n, -1/k) for k > 0, if k = 0 then T(n, k) = k^n.
Original entry on oeis.org
1, 0, -1, 0, 0, -1, 0, 1, 1, -1, 0, 1, 9, 19, 25, 0, -2, 23, 128, 343, 674, 0, -9, -25, 379, 2133, 6551, 15211, 0, -9, -583, -1549, 3603, 33479, 123821, 331827, 0, 50, -3087, -32600, -112975, -174114, 120865, 1619108, 5987745
Offset: 0
Triangle starts:
[0] 1
[1] 0, -1
[2] 0, 0, -1
[3] 0, 1, 1, -1
[4] 0, 1, 9, 19, 25
[5] 0, -2, 23, 128, 343, 674
[6] 0, -9, -25, 379, 2133, 6551, 15211
[7] 0, -9, -583, -1549, 3603, 33479, 123821, 331827
[8] 0, 50, -3087, -32600, -112975, -174114, 120865, 1619108, 5987745
-
A350261 := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, -1/k)):
seq(seq(A350261(n, k), k = 0..n), n = 0..8);
-
T[n_, k_] := If[k == 0, k^n, k^n BellB[n, -1/k]];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
A350262
Triangle read by rows. T(n, k) = B(n, n - k + 1) where B(n, k) = k^n * BellPolynomial(n, -1/k) for k > 0, if k = 0 then B(n, k) = k^n.
Original entry on oeis.org
1, -1, -1, -2, -1, 0, -5, -1, 1, 1, 21, 25, 19, 9, 1, 1103, 674, 343, 128, 23, -2, 29835, 15211, 6551, 2133, 379, -25, -9, 739751, 331827, 123821, 33479, 3603, -1549, -583, -9, 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50
Offset: 0
[0] 1
[1] -1, -1
[2] -2, -1, 0
[3] -5, -1, 1, 1
[4] 21, 25, 19, 9, 1
[5] 1103, 674, 343, 128, 23, -2
[6] 29835, 15211, 6551, 2133, 379, -25, -9
[7] 739751, 331827, 123821, 33479, 3603, -1549, -583, -9
[8] 16084810, 5987745, 1619108, 120865, -174114, -112975, -32600, -3087, 50
-
B := (n, k) -> ifelse(k = 0, k^n, k^n * BellB(n, -1/k)):
A350262 := (n, k) -> B(n, n - k + 1):
seq(seq(A350262(n, k), k = 0..n), n = 0..8);
-
B[n_, k_] := If[k == 0, k^n, k^n BellB[n, -1/k]]; T[n_, k_] := B[n, n - k + 1];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten
Showing 1-5 of 5 results.