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

1, 1, 5, 52, 1445, 104116, 16379797, 6067246144, 5270005429705, 9832425683734288, 40944833826904310921, 384044953998005246634304, 7656468877618298485395299533, 332312769563869315072667521436992, 31885558406529826494376921134421228189

Offset: 0

Author

Alois P. Heinz, Dec 16 2016

Keywords

• nonn

Comments

Number of labeled magmas with n elements satisfying the equation x(yz) = xz. - Andrew Howroyd, Apr 24 2023

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..76
• Wikipedia, Kronecker delta

Crossrefs

Main diagonal of A279636.

Cf. A362384.

Programs

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 *)

Formula

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