A258311 Row sums of A258310.

1, 1, 3, 7, 26, 86, 392, 1660, 9065, 46705, 297984, 1805926, 13186497, 91788477, 754481662, 5924676900, 54092804430, 472512732558, 4739696836485, 45540919862179, 497377234156959, 5208759709993591, 61475622078245542, 696384168181553136, 8825761698420052542

Offset: 0

Author

Alois P. Heinz, May 25 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A258310.

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, false, k) +b(x-1, y+1, true, k)))
    end:
A:= (n, k)-> b(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/2) end:
seq(a(n), n=0..30);

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, False, k] + b[x - 1, y + 1, True, k]]];
A[n_, k_] := b[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/2}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 01 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..floor(n/2)} A258310(n,k).