A192441 Coefficient of x^(2*n) in the expansion of (1 + x^3 + x^4)^n.

1, 0, 2, 3, 6, 30, 35, 210, 350, 1344, 3402, 9240, 29139, 72072, 231660, 603603, 1814670, 5095376, 14507324, 42401502, 118974466, 349305120, 990073812, 2877816304, 8272748675, 23852438880, 69116072950, 198980348385, 577566713520, 1667118322590, 4834810467135

Offset: 0

Author

Joerg Arndt, Jul 01 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A002426, A192440.

Programs

Magma

P:=PolynomialRing(Integers()); [ Coefficients((1+x^3+x^4)^n)[ 2*n+1 ]: n in [0..30] ]; // Bruno Berselli, Jul 01 2011

Maxima

makelist((coeff(expand((1+x^3+x^4)^n), x, 2*n)), n, 0, 30); /* Bruno Berselli, Jul 01 2011 */

PARI

a(n)=polcoeff((1+x^3+x^4)^n,2*n);

Formula

a(n) = Sum_{k=ceiling(n/2)..floor(2*n/3)} binomial(n,k)*binomial(k,2*n-3*k). - R. J. Mathar, Jul 01 2011