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A258224 Row sums of A258223.

%I A258224 #11 Apr 28 2022 07:53:12
%S A258224 1,2,13,166,3450,105053,4385297,239389538,16497800177,1396841773631,
%T A258224 142194450687440,17100401655609460,2394468068218870494,
%U A258224 385647096554809325098,70702689662684594772871,14623755150209185924416598,3385915623744083331349813602
%N A258224 Row sums of A258223.
%H A258224 Alois P. Heinz, <a href="/A258224/b258224.txt">Table of n, a(n) for n = 0..250</a>
%F A258224 a(n) = Sum_{k=0..n} A258223(n,k).
%p A258224 b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,
%p A258224       `if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (k*x+y)/y, 1)
%p A258224                  + b(x-1, y+1, true, k)  ))
%p A258224     end:
%p A258224 A:= (n, k)-> b(2*n, 0, false, k):
%p A258224 T:= proc(n,k) option remember;
%p A258224        add(A(n, i)*(-1)^(k-i)*binomial(k, i), i=0..k)/k!
%p A258224     end:
%p A258224 a:= proc(n) option remember; add(T(n,k), k=0..n) end:
%p A258224 seq(a(n), n=0..20);
%t A258224 b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || y < 0, 0,
%t A258224      If[x == 0, 1, b[x - 1, y - 1, False, k]*If[t, (k*x + y)/y, 1]
%t A258224                  + b[x - 1, y + 1, True, k]]];
%t A258224 A[n_, k_] := b[2*n, 0, False, k];
%t A258224 T[n_, k_] := Sum[A[n, i]*(-1)^(k - i)*Binomial[k, i], {i, 0, k}]/k!;
%t A258224 a[n_] := Sum[T[n, k], {k, 0, n}];
%t A258224 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Apr 28 2022, after _Alois P. Heinz_ *)
%Y A258224 Cf. A258221, A258223.
%K A258224 nonn
%O A258224 0,2
%A A258224 _Alois P. Heinz_, May 23 2015