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

0,2

Links

Table of n, a(n) for 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).

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}]

Crossrefs

Cf. A002457, A008549, A050158.

Sequence in context: A171310 A225116 A367819 * A370035 A081104 A079028

Adjacent sequences: A296767 A296768 A296769 * A296771 A296772 A296773

Keyword

nonn

Author

Peter Luschny, Dec 22 2017

Status

approved