OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..571
FORMULA
G.f.: Sum_{j>=0} (-3)^j*x^j / Product_{k=1..j} (1 - k*x).
E.g.f.: exp(3*(1 - exp(x))).
a(n) = Sum_{k=0..n} (-3)^k * Stirling2(n,k).
MAPLE
b:= proc(n, m) option remember; `if`(n=0,
(-3)^m, 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 17 2022
MATHEMATICA
Table[Exp[3] Sum[(-3)^k k^n/k!, {k, 0, Infinity}], {n, 0, 25}]
Table[BellB[n, -3], {n, 0, 25}]
nmax = 25; CoefficientList[Series[Sum[(-3)^j x^j/Product[(1 - k x), {k, 1, j}] , {j, 0, nmax}], {x, 0, nmax}], x]
nmax = 25; CoefficientList[Series[Exp[3 (1 - Exp[x])], {x, 0, nmax}], x] Range[0, nmax]!
PROG
(Magma) [1] cat [(&+[((-3)^k*StirlingSecond(m, k)):k in [0..m]]):m in [1..25]]; // Marius A. Burtea, Jul 27 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jul 11 2019
STATUS
approved