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A098772 a(n) = Sum_{k=0..n} binomial(2*n,2*k)^2. 1
1, 2, 38, 452, 6470, 92252, 1352540, 20056584, 300546630, 4537543340, 68923356788, 1052049129144, 16123803193628, 247959261273752, 3824345320438520, 59132290704871952, 916312070771835462, 14226520736453485260, 221256270142955957252, 3446310324328958045400, 53753604366737011495220 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

FORMULA

a(n) = (binomial(4*n, 2*n)+(-1)^n*binomial(2*n, n))/2.

Recurrence: n*(n-1)*(2*n-1)*(5*n^2-15*n+11)*a(n)-4*(n-1)*(30*n^4-120*n^3+161*n^2-82*n+12)*a(n-1)-4*(4*n-7)*(2*n-3)*(4*n-5)*(5*n^2-5*n+1)*a(n-2) = 0.

a(n) ~ 2^(4*n-3/2)/sqrt(Pi*n). - Vaclav Kotesovec, Aug 02 2017

MATHEMATICA

Table[Sum[Binomial[2n, 2k]^2, {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Jan 21 2016 *)

PROG

(Maxima) makelist((binomial(4*n, 2*n)+(-1)^n*binomial(2*n, n))/2, n, 0, 12); /* Emanuele Munarini, Feb 01 2017 */

(PARI) a(n) = sum(k=0, n, binomial(2*n, 2*k)^2); \\ Michel Marcus, Feb 01 2017

CROSSREFS

Cf. A037964, A000984.

Sequence in context: A126731 A216357 A046845 * A207320 A262585 A208240

Adjacent sequences:  A098769 A098770 A098771 * A098773 A098774 A098775

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Oct 03 2004

STATUS

approved

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Last modified April 20 07:46 EDT 2021. Contains 343125 sequences. (Running on oeis4.)