|
%I #8 Dec 07 2020 08:24:35
%S 1,1,3,7,20,63,232,944,4158,19236,91794,446311,2194569,10863768,
%T 53995350,269013587,1342192961,6702368648,33486112079,167353481065,
%U 836536395240,4181989400979,20907870188551,104533122311131,522646929294281,2613178606952285
%N Number of partitions of n with five sorts of part 1 which are introduced in ascending order.
%H Alois P. Heinz, <a href="/A320736/b320736.txt">Table of n, a(n) for n = 0..1433</a>
%p b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
%p Stirling2(n, j), j=0..5), add(b(n-i*j, i-1), j=0..n/i))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..40);
%t b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 5}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
%t a[n_] := b[n, n];
%t a /@ Range[0, 40] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y Column k=5 of A292745.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Oct 20 2018
|
