A369399 - OEIS

%I #15 Feb 16 2024 09:54:05

%S 1,1,1,3,11,31,86,277,937,3095,10275,35091,121662,423286,1481648,

%T 5232315,18601843,66436069,238327939,858805613,3106856141,11277393837,

%U 41062303214,149948280259,549027748390,2015108865850,7412690394406,27324968423054

%N Expansion of (1/x) * Series_Reversion( x / (1+x) * (1-x^3)^2 ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

%F a(n) = (1/(n+1)) * [x^n] ( (1+x) / (1-x^3)^2 )^(n+1). - _Seiichi Manyama_, Feb 16 2024

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)*(1-x^3)^2)/x)

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

%Y Cf. A215340, A369401.

%Y Cf. A369296, A370214.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jan 22 2024