A258221 Row sums of A258220.

1, 2, 11, 90, 952, 12203, 182677, 3118314, 59688447, 1265193199, 29408221404, 743677646836, 20325564686926, 597051775012306, 18758388926380409, 627712133246362442, 22288938527631882996, 837033514431748421053, 33146037056721682537319, 1380365444443138768970878

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. A258220, A258224.

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, (x+k*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..25);

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, (x + k*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, 25}] (* Jean-François Alcover, Apr 28 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..n} A258220(n,k).