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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-François 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.)