# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a372461 Showing 1-1 of 1 %I A372461 #6 May 02 2024 09:46:21 %S A372461 1,4,36,370,4012,44814,510198,5886206,68579020,805045276,9507007686, %T A372461 112817021332,1344160003030,16069300956726,192662610805386, %U A372461 2315694030560640,27893938099222316,336643301659031102,4069747367955175236,49274614400855690158 %N A372461 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3) )^(2*n). %F A372461 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(5*n-2*k-1,n-3*k). %F A372461 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^3)^2 ). See A368968. %o A372461 (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k)); %Y A372461 Cf. A368968, A372465. %K A372461 nonn %O A372461 0,2 %A A372461 _Seiichi Manyama_, May 01 2024 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE