|
%I #10 May 27 2018 06:51:18
%S 1,57,1839,44346,891892,15848311,257647088,3921554995,56796169899,
%T 792102157717,10734723141617,142380931674179,1858965371935248,
%U 24006134113802346,307860388231938976,3934302726222970593,50254089923100713719,643301179860716506788
%N Sum of the sizes of the tenth blocks in all set partitions of {1,2,...,n}.
%H Alois P. Heinz, <a href="/A270502/b270502.txt">Table of n, a(n) for n = 10..575</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p b:= proc(n, m) option remember; `if`(n=0, [1, 0],
%p add((p->`if`(j<11, [p[1], p[2]+p[1]*x^j], p))(
%p b(n-1, max(m, j))), j=1..m+1))
%p end:
%p a:= n-> coeff(b(n, 0)[2], x, 10):
%p seq(a(n), n=10..30);
%t b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 11, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
%t a[n_] := Coefficient[b[n, 0][[2]], x, 10];
%t Table[a[n], {n, 10, 30}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)
%Y Column p=10 of A270236.
%K nonn
%O 10,2
%A _Alois P. Heinz_, Mar 18 2016
|
