A303914 a(n) = [x^n] (1/(1 - x))*Product_{k>=1} 1/(1 - n*x^k).

1, 2, 9, 55, 465, 5051, 69265, 1147287, 22307905, 497211049, 12484203601, 348391613615, 10691846920081, 357749800027465, 12958472141161457, 505088781523073326, 21076091000708067585, 937322034938743608556, 44256147057318887809993, 2210813717869831566759857, 116492226446226314836976401

Offset: 0

Author

Ilya Gutkovskiy, May 02 2018

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000070, A124577, A246935, A303070.

Programs

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}]

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