A396199 a(n) = (n + 1)*(2^(n + 1) - binomial(n, floor(n / 2))), row sums of A396200.

1, 6, 18, 52, 130, 324, 756, 1768, 3978, 8980, 19756, 43608, 94484, 205352, 440040, 945616, 2009434, 4281012, 9037692, 19123960, 40160316, 84514936, 176713048, 370203312, 771256900, 1609622664, 3343062456, 6954560368, 14405875048, 29885491920, 61763349968, 127821667232

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Formula

From Vaclav Kotesovec, May 19 2026: (Start)

Recurrence: (n-1)*n*a(n) = 2*(n-1)*(n+1)*a(n-1) + 4*(n-2)*n*a(n-2) - 8*(n-1)*n*a(n-3).

a(n) ~ n * 2^(n+1).

a(n) = (n+1)*2^(n+1) - 4*(n+1)*Gamma(n)/(n*Gamma(n/2)^2) if n is even and n>0.

a(n) = (n+1)*2^(n+1) - 2*n*Gamma(n)/Gamma((n+1)/2)^2 if n is odd. (End)

Maple

a := n -> (n + 1)*(2^(n + 1) - binomial(n, iquo(n, 2))):
seq(a(n), n = 0..31);

Mathematica

Table[Sum[Sum[Binomial[2*i, i] * Binomial[n-2*i, k-i], {i, 0, n}], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, May 19 2026 *)
(* Alternative: *)
A396199[n_] := (n + 1)*(2^(n + 1) - Binomial[n, Quotient[n, 2]]);
Array[A396199, 35, 0] (* Paolo Xausa, May 19 2026 *)

Crossrefs

Cf. A396200.

Sequence in context: A015645 A001216 A396891 * A318484 A079843 A290582

Adjacent sequences: A396196 A396197 A396198 * A396200 A396201 A396202

Keyword

nonn

Author

Peter Luschny, May 19 2026

Status

approved