A309652 a(n) = [x^n] B(x)^n, where B(x) is g.f. of A000312.

1, 1, 9, 106, 1493, 24276, 448122, 9301251, 215547845, 5541171496, 156997349684, 4870353700532, 164366482285898, 5998207807965543, 235388194276592723, 9884482616014596546, 442206843338189113445, 20995082225203329126384, 1054247070579064423466016

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..385

Formula

a(n) ~ exp(exp(-1)) * n^(n+1).

Maple

B:= proc(n) option remember; n^n end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1, B(n),
      (h-> add(b(j, h)*b(n-j, i-h), j=0..n))(iquo(i, 2))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 23 2019

Mathematica

Table[SeriesCoefficient[(1+Sum[k^k*x^k, {k, 1, n}])^n, {x, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A287899, A326985, A326986.

Sequence in context: A052503 A261428 A122569 * A357295 A367789 A316145

Adjacent sequences: A309649 A309650 A309651 * A309653 A309654 A309655

Keyword

nonn

Author

Vaclav Kotesovec, Aug 11 2019

Status

approved