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

0,2

Links

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

Formula

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

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 *)

Crossrefs

Cf. A258220, A258224.

Sequence in context: A197914 A371537 A138552 * A004677 A266656 A094955

Adjacent sequences: A258218 A258219 A258220 * A258222 A258223 A258224

Keyword

nonn

Author

Alois P. Heinz, May 23 2015

Status

approved