|
%I #10 May 01 2024 08:59:31
%S 1,1,7,34,191,1071,6154,35729,209455,1236508,7341577,43792112,
%T 262230242,1575391156,9490934411,57316715079,346875036879,
%U 2103174805035,12773139313516,77689736488088,473160660856361,2885208137132852,17612514244078288,107621658416373752
%N Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2)^2 )^n.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(2*n-k-1,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-x^2)^2 / (1-x) ). See A369486.
%o (PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
%Y Cf. A370617, A370619.
%Y Cf. A369486.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 30 2024
|
