A370172 - OEIS

%I #12 Feb 11 2024 09:16:23

%S 1,5,51,581,6963,85905,1079943,13756216,176939187,2292988919,

%T 29892396451,391576960230,5150057095527,67962810381653,

%U 899458144305408,11933576896320981,158672857603511987,2113800649819533735,28207266176359605705,376976971371883606824

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

%F a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(5*n-k,n-2*k).

%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^2)^3) ). See A369480.

%o (PARI) a(n, s=2, t=3, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));

%Y Cf. A370170, A370171.

%Y Cf. A369480.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 11 2024