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A258224
Row sums of A258223.
3
1, 2, 13, 166, 3450, 105053, 4385297, 239389538, 16497800177, 1396841773631, 142194450687440, 17100401655609460, 2394468068218870494, 385647096554809325098, 70702689662684594772871, 14623755150209185924416598, 3385915623744083331349813602
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} A258223(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+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..20);
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 + 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, 20}] (* Jean-François Alcover, Apr 28 2022, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A132521 A360601 A177448 * A351021 A078363 A143851
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 23 2015
STATUS
approved