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A296771 Row sums of A050157. 2
1, 3, 13, 58, 257, 1126, 4882, 20980, 89497, 379438, 1600406, 6720748, 28117498, 117254268, 487589572, 2022568168, 8371423177, 34581780478, 142605399982, 587138954428, 2413944555742, 9911778919348, 40650232625212, 166534680737368, 681576405563722 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..1657

FORMULA

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

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

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

a(n) = A037965(n+1) - A000346(n-1) for n >= 1.

From Robert Israel, Dec 21 2017: (Start)

a(n) = (n+3/2)*binomial(2*n,n) - 2^(2*n-1).

G.f.: (3/2-4*x)*(1-4*x)^(-3/2) - (1/2)*(1-4*x)^(-1).

64*(n+1)*(2*n+1)*a(n)-8*(2*n+3)*(5*n+4)*a(n+1)+2*(n+2)*(8*n+11)*a(n+2)-(n+3)*(n+2)*a(n+3)=0. (End)

MAPLE

A296771 := n -> add(binomial(2*n, n) - binomial(2*n, n+k+1), k=0..n):

seq(A296771(n), n=0..24);

MATHEMATICA

a[n_] := 4^n ((n - 1/2)! (2 n + 3)/(2 Sqrt[Pi] n!) - 1/2);

Table[a[n], {n, 0, 24}]

PROG

(PARI) a(n) = sum(k=0, n, binomial(2*n, n) - binomial(2*n, n+k+1)) \\ Iain Fox, Dec 21 2017

CROSSREFS

Cf. A000346, A037965, A050157, A296770.

Sequence in context: A151224 A151225 A326984 * A270786 A151226 A151320

Adjacent sequences:  A296768 A296769 A296770 * A296772 A296773 A296774

KEYWORD

nonn

AUTHOR

Peter Luschny, Dec 21 2017

STATUS

approved

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Last modified August 14 04:13 EDT 2020. Contains 336477 sequences. (Running on oeis4.)