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A258221 Row sums of A258220.

%I A258221 #10 Apr 28 2022 07:52:21
%S A258221 1,2,11,90,952,12203,182677,3118314,59688447,1265193199,29408221404,
%T A258221 743677646836,20325564686926,597051775012306,18758388926380409,
%U A258221 627712133246362442,22288938527631882996,837033514431748421053,33146037056721682537319,1380365444443138768970878
%N A258221 Row sums of A258220.
%H A258221 Alois P. Heinz, <a href="/A258221/b258221.txt">Table of n, a(n) for n = 0..250</a>
%F A258221 a(n) = Sum_{k=0..n} A258220(n,k).
%p A258221 b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,
%p A258221       `if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (x+k*y)/y, 1)
%p A258221                  + b(x-1, y+1, true, k)  ))
%p A258221     end:
%p A258221 A:= (n, k)-> b(2*n, 0, false, k):
%p A258221 T:= proc(n,k) option remember;
%p A258221        add(A(n, i)*(-1)^(k-i)*binomial(k, i), i=0..k)/k!
%p A258221     end:
%p A258221 a:= proc(n) option remember; add(T(n,k), k=0..n) end:
%p A258221 seq(a(n), n=0..25);
%t A258221 b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || y < 0, 0,
%t A258221      If[x == 0, 1, b[x - 1, y - 1, False, k]*If[t, (x + k*y)/y, 1]
%t A258221                  + b[x - 1, y + 1, True, k]]];
%t A258221 A[n_, k_] := b[2*n, 0, False, k];
%t A258221 T[n_, k_] := Sum[A[n, i]*(-1)^(k - i)*Binomial[k, i], {i, 0, k}]/k!;
%t A258221 a[n_] := Sum[T[n, k], {k, 0, n}];
%t A258221 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 28 2022, after _Alois P. Heinz_ *)
%Y A258221 Cf. A258220, A258224.
%K A258221 nonn
%O A258221 0,2
%A A258221 _Alois P. Heinz_, May 23 2015