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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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000142, A107895, A168246, A261053, A026007, A027998, A248882, A102866, A256142.

Sequence in context: A150828 A308336 A120774 * A128324 A264572 A279692

Adjacent sequences:  A261049 A261050 A261051 * A261053 A261054 A261055

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 08 2015

STATUS

approved

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Last modified February 24 22:04 EST 2020. Contains 332216 sequences. (Running on oeis4.)