A258224 Row sums of A258223.

1, 2, 13, 166, 3450, 105053, 4385297, 239389538, 16497800177, 1396841773631, 142194450687440, 17100401655609460, 2394468068218870494, 385647096554809325098, 70702689662684594772871, 14623755150209185924416598, 3385915623744083331349813602

Offset: 0

Author

Alois P. Heinz, May 23 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A258221, A258223.

Programs

Maple

b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,
      `if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (k*x+y)/y, 1)
                 + b(x-1, y+1, true, k)  ))
    end:
A:= (n, k)-> b(2*n, 0, false, k):
T:= proc(n,k) option remember;
       add(A(n, i)*(-1)^(k-i)*binomial(k, i), i=0..k)/k!
    end:
a:= proc(n) option remember; add(T(n,k), k=0..n) end:
seq(a(n), n=0..20);

Mathematica

b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || y < 0, 0,
     If[x == 0, 1, b[x - 1, y - 1, False, k]*If[t, (k*x + y)/y, 1]
                 + b[x - 1, y + 1, True, k]]];
A[n_, k_] := b[2*n, 0, False, k];
T[n_, k_] := Sum[A[n, i]*(-1)^(k - i)*Binomial[k, i], {i, 0, k}]/k!;
a[n_] := Sum[T[n, k], {k, 0, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Apr 28 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..n} A258223(n,k).