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URL: https://oeis.org/A303914

⇱ A303914 - OEIS

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A303914
a(n) = [x^n] (1/(1 - x))*Product_{k>=1} 1/(1 - n*x^k).
1
1, 2, 9, 55, 465, 5051, 69265, 1147287, 22307905, 497211049, 12484203601, 348391613615, 10691846920081, 357749800027465, 12958472141161457, 505088781523073326, 21076091000708067585, 937322034938743608556, 44256147057318887809993, 2210813717869831566759857, 116492226446226314836976401
OFFSET
0,2
FORMULA
a(n) = [x^n] (1/(1 - x))*exp(Sum_{k>=1} n^k*x^k/(k*(1 - x^k))).
a(n) = Sum_{j=0..n} A246935(j,n).
a(n) ~ n^n. - Vaclav Kotesovec, May 04 2018
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
end:
a:= n-> add(b(j$2, n), j=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, May 02 2018
MATHEMATICA
Table[SeriesCoefficient[1/(1 - x) Product[1/(1 - n x^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/(1 - x) Exp[Sum[n^k x^k/(k (1 - x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 02 2018
STATUS
approved