OFFSET
0,3
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..572
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Eric Weisstein's MathWorld, Stirling Transform
FORMULA
EXAMPLE
E.g.f.: A(x) = x/1! + 9*x^2/2! + 52*x^3/3! + 283*x^4/4! + 1561*x^5/5! + 8930*x^6/6! + ...
MAPLE
b:= proc(n, m) option remember; `if`(n=0,
m^3, m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..27); # Alois P. Heinz, Jul 15 2022
MATHEMATICA
Range[0, 23]! CoefficientList[Series[Exp[Exp[x] - 1] (Exp[3 x] - 2 Exp[x] + 1), {x, 0, 23}], x]
Table[Sum[StirlingS2[n, k] k^3, {k, 0, n}], {n, 0, 23}]
Table[Sum[Binomial[n, k] BellB[n-k] (3^k - 2), {k, 1, n}], {n, 0, 23}]
Table[BellB[n+3] - 3*BellB[n+2] + BellB[n], {n, 0, 23}] (* Vaclav Kotesovec, Aug 06 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 08 2017
STATUS
approved