OFFSET
0,3
COMMENTS
Weigh transform of the factorial numbers. - Alois P. Heinz, Jun 11 2018
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
FORMULA
a(n) ~ n! * (1 + 1/n + 2/n^2 + 10/n^3 + 57/n^4 + 401/n^5 + 3382/n^6 + 33183/n^7 + 371600/n^8 + 4685547/n^9 + 65792453/n^10).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(i!, j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25); # Alois P. Heinz, Aug 08 2015
MATHEMATICA
nmax=25; CoefficientList[Series[Product[(1+x^k)^(k!), {k, 1, nmax}], {x, 0, nmax}], x]
PROG
(PARI) seq(n)={Vec(exp(x*Ser(dirmul(vector(n, n, n!), -vector(n, n, (-1)^n/n)))))} \\ Andrew Howroyd, Jun 22 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 08 2015
STATUS
approved