A296770 Row sums of A050158.

1, 5, 24, 111, 500, 2210, 9632, 41531, 177564, 754014, 3184016, 13382710, 56026984, 233765636, 972504704, 4035441491, 16707488684, 69033916166, 284733161264, 1172510645666, 4821324991064, 19799091571676, 81208982686784, 332726301861086, 1361862906980120

Offset: 0

Author

Peter Luschny, Dec 22 2017

Keywords

• nonn

Crossrefs

Cf. A002457, A008549, A050158.

Programs

Maple

A296770 := n -> add(binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1), k=0..n):
seq(A296770(n), n=0..24);

Mathematica

a[n_] := 4^n ((2 (2 + n) Gamma[3/2 + n])/(Sqrt[Pi] Gamma[2 + n]) - 1);
Table[a[n], {n, 0, 24}]

Formula

a(n) = Sum_{k=0..n} (binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1)).

a(n) = 4^n*((2*(n + 2)*Gamma(n + 3/2))/(sqrt(Pi)*Gamma(n + 2)) - 1).

a(n) = (n/2+1)*binomial(2*(n+1), n+1) - 4^n.

a(n) ~ 4^n*(2*sqrt(n/Pi) - 1).

a(n) = A002457(n) - A008549(n).