cp's OEIS Frontend

A279644 a(n) is the n-th term of the exponential transform of the n-th powers.

%I A279644 #14 Apr 26 2023 10:28:15
%S A279644 1,1,5,52,1445,104116,16379797,6067246144,5270005429705,
%T A279644 9832425683734288,40944833826904310921,384044953998005246634304,
%U A279644 7656468877618298485395299533,332312769563869315072667521436992,31885558406529826494376921134421228189
%N A279644 a(n) is the n-th term of the exponential transform of the n-th powers.
%C A279644 Number of labeled magmas with n elements satisfying the equation x(yz) = xz. - _Andrew Howroyd_, Apr 24 2023
%H A279644 Alois P. Heinz, <a href="/A279644/b279644.txt">Table of n, a(n) for n = 0..76</a>
%H A279644 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kronecker_delta">Kronecker delta</a>
%F A279644 a(n) = n! * [x^n] exp(exp(x)*(Sum_{j=0..n} Stirling2(n,j)*x^j) - delta_{0,n}).
%p A279644 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A279644       add(binomial(n-1, j-1)*j^k*b(n-j, k), j=1..n))
%p A279644     end:
%p A279644 a:= n-> b(n$2):
%p A279644 seq(a(n), n=0..15);
%t A279644 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}]];
%t A279644 a[n_] := b[n, n];
%t A279644 Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Jun 01 2018, from Maple *)
%Y A279644 Main diagonal of A279636.
%Y A279644 Cf. A362384.
%K A279644 nonn
%O A279644 0,3
%A A279644 _Alois P. Heinz_, Dec 16 2016