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A261052
Expansion of Product_{k>=1} (1+x^k)^(k!).
5
1, 1, 2, 8, 31, 157, 915, 6213, 48240, 423398, 4147775, 44882107, 531564195, 6837784087, 94909482330, 1413561537884, 22482554909451, 380269771734265, 6815003300096013, 128992737080703803, 2571218642722865352, 53835084737513866662, 1181222084520177393143
OFFSET
0,3
COMMENTS
Weigh transform of the factorial numbers. - Alois P. Heinz, Jun 11 2018
LINKS
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 08 2015
STATUS
approved