OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} binomial(n-1,k-1) * A005651(k) * n! / k!.
a(n) ~ c * 2^(n-1) * n!, where c = A247551 = 2.52947747207915264818... - Vaclav Kotesovec, Feb 16 2020
MATHEMATICA
nmax = 19; CoefficientList[Series[Product[1/(1 - x^k/(k! (1 - x)^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n - 1, k - 1] Total[Apply[Multinomial, IntegerPartitions[k], {1}]] n!/k!, {k, 0, n}], {n, 0, 19}]
PROG
(PARI) seq(n)={Vec(serlaplace(prod(k=1, n, 1 / (1 - x^k/(k!*(1 - x)^k)) + O(x*x^n))))} \\ Andrew Howroyd, Feb 13 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 13 2020
STATUS
approved