A258308 Row sums of A258307.

1, 1, 3, 7, 24, 74, 277, 997, 4016, 16029, 68802, 296740, 1347175, 6185975, 29530010, 143008050, 714469780, 3625572745, 18884279461, 99936069760, 540947985741, 2974463266900, 16686653393208, 95053009906135, 551356966419818, 3245644584299434, 19425857465136193

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. A258307.

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, 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:= n-> add(T(n, k), k=0..n/2):
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, (x + k*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_] := 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, Apr 30 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..floor(n/2)} A258307(n,k).