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A327870 Row sums of A327869.

%I A327870 #11 Mar 28 2022 08:13:07
%S A327870 1,2,2,11,14,47,305,611,2070,8831,84077,204371,944333,3850407,
%T A327870 23991739,297448526,927586630,4775902567,24534836837,141681919871,
%U A327870 1080484165089,18553632475991,66762080435239,415657332495526,2298883231736949,15799818116227747
%N A327870 Row sums of A327869.
%H A327870 Alois P. Heinz, <a href="/A327870/b327870.txt">Table of n, a(n) for n = 0..500</a>
%p A327870 b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0,
%p A327870      `if`(n=0, 1, `if`(i<2, 0, b(n, i-1, `if`(i=k, 0, k)))+
%p A327870      `if`(i=k, 0, b(n-i, min(n-i, i-1), k)*binomial(n, i))))
%p A327870     end:
%p A327870 a:= n-> b(n$2, 0)*(n+1) -add(b(n$2, k), k=1..n):
%p A327870 seq(a(n), n=0..28);
%t A327870 b[n_, i_, k_] := b[n, i, k] = If[i*(i + 1)/2 < n, 0,
%t A327870      If[n == 0, 1, If[i < 2, 0, b[n, i - 1, If[i == k, 0, k]]] +
%t A327870      If[i == k, 0, b[n - i, Min[n - i, i - 1], k]*Binomial[n, i]]]];
%t A327870 a[n_] := b[n, n, 0]*(n + 1) - Sum[b[n, n, k], {k, 1, n}];
%t A327870 Table[a[n], {n, 0, 28}] (* _Jean-François Alcover_, Mar 28 2022, after _Alois P. Heinz_ *)
%Y A327870 Row sums of A327869.
%Y A327870 Cf. A320566.
%K A327870 nonn
%O A327870 0,2
%A A327870 _Alois P. Heinz_, Sep 28 2019