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A365821 Total number of partitions of [n-s] whose block minima sum to s, summed over all s.

%I A365821 #14 Dec 16 2023 20:12:21
%S A365821 1,0,1,1,1,2,3,6,11,23,46,97,205,448,1004,2339,5661,14291,37507,
%T A365821 101962,285386,817772,2386946,7069893,21195092,64225525,196636559,
%U A365821 608551084,1905848637,6049696252,19501015441,63960251538,213822965681,729536174204,2541833303563
%N A365821 Total number of partitions of [n-s] whose block minima sum to s, summed over all s.
%H A365821 Alois P. Heinz, <a href="/A365821/b365821.txt">Table of n, a(n) for n = 0..350</a>
%H A365821 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A365821 a(7) = 6: 12|3, 134|2, 13|24, 14|23, 1|234, 123456.
%F A365821 a(8) = 11: 124|3, 12|34, 1345|2, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234, 1|2345, 1234567.
%p A365821 b:= proc(n, i, t, m) option remember; `if`(n=0, t^(m-i+1),
%p A365821      `if`((i+m)*(m+1-i)/2<n or i>n, 0, `if`(t=0, 0,
%p A365821       t*b(n, i+1, t, m))+ b(n-i, i+1, t+1, m)))
%p A365821     end:
%p A365821 a:= n-> add(b(k, 1, 0, n-k), k=0..n):
%p A365821 seq(a(n), n=0..42);
%Y A365821 Antidiagonal sums of A124327.
%Y A365821 Cf. A368102.
%K A365821 nonn
%O A365821 0,6
%A A365821 _Alois P. Heinz_, Dec 14 2023