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A137636 a(n) = Sum_{k=0..n} C(2k+1,k)*C(2k+1,n-k) ; equals row 1 of square array A137634; also equals the convolution of A137635 and A073157. 4
1, 4, 19, 94, 474, 2431, 12609, 65972, 347524, 1840680, 9792986, 52296799, 280163091, 1504969409, 8103433329, 43722788132, 236340999038, 1279602656590, 6938126362948, 37668424608552, 204751452911832, 1114151447523038 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

FORMULA

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

PROG

(PARI) {a(n)=sum(k=0, n, binomial(2*k+1, k)*binomial(2*k+1, 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, n, x)}

CROSSREFS

Cf. A137634, A137635, A137637, A137638, A073157.

Sequence in context: A122369 A005978 A083065 * A027618 A278678 A020060

Adjacent sequences:  A137633 A137634 A137635 * A137637 A137638 A137639

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 31 2008

STATUS

approved

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Last modified December 15 09:53 EST 2018. Contains 318148 sequences. (Running on oeis4.)