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

0,3

Links

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

Formula

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

Crossrefs

Cf. A258310.

Sequence in context: A148740 A148741 A328280 * A184459 A215018 A069738

Adjacent sequences: A258308 A258309 A258310 * A258312 A258313 A258314

Keyword

nonn

Author

Alois P. Heinz, May 25 2015

Status

approved