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A259843 Number of 1 elements in all n X n Tesler matrices of nonnegative integers.

%I A259843 #12 May 15 2022 07:40:40
%S A259843 1,3,15,117,1367,23329,570933,19740068,951916938,63295826369,
%T A259843 5743788894259,704672958229270,115877288304781885,
%U A259843 25338423080304873558,7313716095786704678585,2767636572798780219442327,1364367542961142350256304582,871016593387715393187604249892
%N A259843 Number of 1 elements in all n X n Tesler matrices of nonnegative integers.
%C A259843 For the definition of Tesler matrices see A008608.
%F A259843 a(n) = A259841(n,1).
%e A259843 There are two 2 X 2 Tesler matrices: [1,0; 0,1], [0,1; 0,2], containing three 1's, thus a(2) = 3.
%p A259843 g:= u-> `if`(u=1, 1, 0):
%p A259843 b:= proc(n, i, l) option remember; (m->`if`(m=0, [1, g(n)], `if`(i=0,
%p A259843      (p->p+[0, p[1]*g(n)])(b(l[1]+1, m-1, subsop(1=NULL, l))), add(
%p A259843      (p->p+[0, p[1]*g(j)])(b(n-j, i-1, subsop(i=l[i]+j, l)))
%p A259843       , j=0..n))))(nops(l))
%p A259843     end:
%p A259843 a:= n-> b(1, n-1, [0$(n-1)])[2]:
%p A259843 seq(a(n), n=1..14);
%t A259843 g[u_] := If[u == 1, 1, 0];
%t A259843 b[n_, i_, l_] := b[n, i, l] = Function[m, If[m == 0, {1, g[n]}, If[i == 0, # + {0, #[[1]] g[n]}&[b[l[[1]] + 1, m - 1, ReplacePart[l, 1 -> Nothing]] ], Sum[# + {0, #[[1]] g[j]}&[b[n - j, i - 1, ReplacePart[l, i -> l[[i]] + j]]], {j, 0, n}]]]][Length[l]];
%t A259843 a[n_] := b[1, n - 1, Table[0, {n - 1}]][[2]];
%t A259843 Table[Print[n, " ", a[n]]; a[n], {n, 1, 18}] (* _Jean-François Alcover_, May 15 2022, after _Alois P. Heinz_ *)
%Y A259843 Column k=1 of A259841.
%K A259843 nonn
%O A259843 1,2
%A A259843 _Alois P. Heinz_, Jul 06 2015