A137637 - OEIS

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A137637

a(n) = Sum_{k=0..n} C(2k+2,k)*C(2k+2,n-k) ; equals row 2 of square array A137634 ; also equals the convolution of A137635 and the self-convolution of A073157.

1, 6, 32, 170, 899, 4764, 25318, 134964, 721562, 3868024, 20785035, 111931154, 603938905, 3264309644, 17671408012, 95800342628, 520022296700, 2826089180652, 15374990077568, 83727902852188, 456370687687082

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: A(x) = R(x)*G(x)^2, where R(x) = 1/sqrt(1-4*x*(1+x)^2) is the g.f. of A137635 and G(x) = (1-sqrt(1-4*x*(1+x)^2))/(2*x*(1+x)) is the g.f. of A073157.

PROG

(PARI) {a(n)=sum(k=0, n, binomial(2*k+2, k)*binomial(2*k+2, n-k))} /* Using the g.f.: */ {a(n)=local(R=1/sqrt(1-4*x*(1+x +x*O(x^n))^2), G=(1-sqrt(1-4*x*(1+x)^2+x^2*O(x^n)))/(2*x*(1+x+x*O(x^n)))); polcoeff(R*G^2, n, x)}

CROSSREFS

Cf. A137634, A137635, A137636, A137638, A073157.

Sequence in context: A084326 A199699 A306900 * A125190 A264460 A180037

Adjacent sequences: A137634 A137635 A137636 * A137638 A137639 A137640

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 31 2008

STATUS

approved