|
|
A308491
|
|
a(0) = 1, a(n) = Sum_{k=1..n} stirling2(n,k) * k^(3*k).
|
|
3
|
|
|
1, 1, 65, 19876, 16895763, 30685843321, 102018812632786, 560682901512212459, 4738032814084465062121, 58320000513552476843995786, 1002620283226568243192938115197, 23280221638971518379191182864465213, 710336441472841166799952152725333251616
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ n^(3*n).
E.g.f.: Sum_{k>=0} (k^3 * (exp(x) - 1))^k / k!. - Seiichi Manyama, Feb 04 2022
|
|
MATHEMATICA
|
Join[{1}, Table[Sum[k^(3*k)*StirlingS2[n, k], {k, 1, n}], {n, 1, 15}]]
|
|
PROG
|
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^3*(exp(x)-1))^k/k!))) \\ Seiichi Manyama, Feb 04 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|