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A137635 a(n) = Sum_{k=0..n} C(2k,k)*C(2k,n-k); equals row 0 of square array A137634. 4
1, 2, 10, 46, 226, 1136, 5810, 30080, 157162, 826992, 4376408, 23267332, 124179570, 664919780, 3570265000, 19216805476, 103652442922, 560127574340, 3031887311256, 16435458039076, 89213101943000, 484839755040768 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Diagonal of rational function 1/(1 - (x + y + x^2*y + x*y^2)). - Gheorghe Coserea, Aug 31 2018

LINKS

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

FORMULA

G.f.: A(x) = 1/sqrt(1 - 4x(1+x)^2).

D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +8*(-n+1)*a(n-2) +2*(-2*n+3)*a(n-3)=0. - R. J. Mathar, Jan 14 2020

MATHEMATICA

CoefficientList[Series[1/Sqrt[1 - 4*x*(1 + x)^2], {x, 0, 50}], x] (* Stefano Spezia, Sep 01 2018 *)

Table[Sum[Binomial[2k, k]Binomial[2k, n-k], {k, 0, n}], {n, 0, 30}] (* Harvey P. Dale, Dec 31 2018 *)

PROG

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

CROSSREFS

Cf. A137634, A137636, A137637, A137638, A073157.

Sequence in context: A221196 A137193 A006213 * A029706 A191644 A009640

Adjacent sequences:  A137632 A137633 A137634 * A137636 A137637 A137638

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 31 2008

STATUS

approved

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Last modified February 17 12:14 EST 2020. Contains 331996 sequences. (Running on oeis4.)