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A296770 Row sums of A050158. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A183934 A171310 A225116 * A081104 A079028 A218987

Adjacent sequences:  A296767 A296768 A296769 * A296771 A296772 A296773

KEYWORD

nonn

AUTHOR

Peter Luschny, Dec 22 2017

STATUS

approved

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Last modified October 22 12:30 EDT 2019. Contains 328318 sequences. (Running on oeis4.)