A370275 - OEIS

%I #9 Feb 14 2024 10:48:24

%S 1,2,10,62,394,2552,16822,112310,756874,5137676,35076360,240606082,

%T 1656906550,11447855850,79319081054,550925792312,3834743187594,

%U 26742188401900,186802789016908,1306827910585782,9154542088193544,64206944261628146,450823141806229290

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

%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(3*n-3*k-1,n-3*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^3)^2 ). See A369298.

%o (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));

%Y Cf. A369298.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 13 2024