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A279644 a(n) is the n-th term of the exponential transform of the n-th powers. 4
1, 1, 5, 52, 1445, 104116, 16379797, 6067246144, 5270005429705, 9832425683734288, 40944833826904310921, 384044953998005246634304, 7656468877618298485395299533, 332312769563869315072667521436992, 31885558406529826494376921134421228189 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..76

Wikipedia, Kronecker delta

FORMULA

a(n) = n! * [x^n] exp(exp(x)*(Sum_{j=0..n} Stirling2(n,j)*x^j) - delta_{0,n}).

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1,

      add(binomial(n-1, j-1)*j^k*b(n-j, k), j=1..n))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..15);

MATHEMATICA

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[Binomial[n-1, j-1]*j^k*b[n-j, k], {j, 1, n}]];

a[n_] := b[n, n];

Table[a[n], {n, 0, 15}] (* Jean-Fran├žois Alcover, Jun 01 2018, from Maple *)

CROSSREFS

Main diagonal of A279636.

Sequence in context: A278879 A322195 A216464 * A001173 A277202 A223248

Adjacent sequences:  A279641 A279642 A279643 * A279645 A279646 A279647

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 16 2016

STATUS

approved

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Last modified June 19 05:33 EDT 2019. Contains 324218 sequences. (Running on oeis4.)