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

%I #18 Sep 08 2022 08:45:57

%S 1,0,2,3,6,30,35,210,350,1344,3402,9240,29139,72072,231660,603603,

%T 1814670,5095376,14507324,42401502,118974466,349305120,990073812,

%U 2877816304,8272748675,23852438880,69116072950,198980348385,577566713520,1667118322590,4834810467135

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

%H Vincenzo Librandi, <a href="/A192441/b192441.txt">Table of n, a(n) for n = 0..200</a>

%F 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

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

%o (Maxima) makelist((coeff(expand((1+x^3+x^4)^n), x, 2*n)), n, 0, 30); /* _Bruno Berselli_, Jul 01 2011 */

%o (Magma) P<x>:=PolynomialRing(Integers()); [ Coefficients((1+x^3+x^4)^n)[ 2*n+1 ]: n in [0..30] ]; // _Bruno Berselli_, Jul 01 2011

%Y Cf. A002426, A192440.

%K nonn

%O 0,3

%A _Joerg Arndt_, Jul 01 2011