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A262910 a(n) = Sum_{k=0..n} binomial(k+n-1,k)*binomial(k+n,2*k). 1
1, 2, 10, 59, 366, 2337, 15205, 100235, 667222, 4474733, 30188335, 204646532, 1392850785, 9511878729, 65144238981, 447263887479, 3077459618886, 21215286546705, 146500755609415, 1013180180867125, 7016536189029551, 48650933146617728, 337709155342663620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1176

FORMULA

G.f.: A(x) = x*B'(x)/B(x), where B(x)/x is g.f. of A007863.

Recurrence: 5*(n-1)*n*(35*n^2 - 143*n + 138)*a(n) = 2*(n-1)*(630*n^3 - 2889*n^2 + 3746*n - 1200)*a(n-1) - 2*(70*n^4 - 426*n^3 + 811*n^2 - 589*n + 150)*a(n-2) + 2*(n-3)*(2*n - 3)*(35*n^2 - 73*n + 30)*a(n-3). - Vaclav Kotesovec, Oct 04 2015

a(n) = hypergeom([-n, n, n+1], [1/2, 1], -1/4). - Peter Luschny, Oct 08 2015

MAPLE

a := n -> hypergeom([-n, n, n+1], [1/2, 1], -1/4):

seq(round(evalf(a(n), 32)), n=0..21); # Peter Luschny, Oct 08 2015

MATHEMATICA

Table[Sum[Binomial[k+n-1, k]*Binomial[k+n, 2*k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 04 2015 *)

PROG

(Maxima)

B(x):=sum(sum(binomial(i+n-1, i)*binomial(i+n, 2*i+1), i, 0, n-1)/n*x^n, n, 1, 30);

taylor(x*diff(B(x), x)/B(x), x, 0, 20);

(PARI) a(n) = sum(k=0, n, binomial(k+n-1, k)*binomial(k+n, 2*k));

vector(50, n, a(n-1)) \\ Altug Alkan, Oct 04 2015

CROSSREFS

Cf. A007863.

Sequence in context: A309955 A340987 A186758 * A202482 A240605 A095993

Adjacent sequences:  A262907 A262908 A262909 * A262911 A262912 A262913

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Oct 04 2015

STATUS

approved

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Last modified February 26 14:18 EST 2021. Contains 341632 sequences. (Running on oeis4.)