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A309652 a(n) = [x^n] B(x)^n, where B(x) is g.f. of A000312. 2
1, 1, 9, 106, 1493, 24276, 448122, 9301251, 215547845, 5541171496, 156997349684, 4870353700532, 164366482285898, 5998207807965543, 235388194276592723, 9884482616014596546, 442206843338189113445, 20995082225203329126384, 1054247070579064423466016 (list; graph; refs; listen; history; text; internal format)
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 * A316145 A039619 A249048

Adjacent sequences:  A309649 A309650 A309651 * A309653 A309654 A309655

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 11 2019

STATUS

approved

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Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)