This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378425 #12 Nov 26 2024 09:32:22
%S A378425 1,1,2,7,24,82,297,1121,4317,16900,67185,270480,1100122,4513809,
%T A378425 18661618,77666327,325117967,1368001765,5782686120,24545144206,
%U A378425 104573104040,447036252525,1916918691196,8243075111450,35538551601880,153584392913986,665201585797986,2887012910233897
%N A378425 Expansion of (1/x) * Series_Reversion( x / (1 + x + x^2 * (1 + x)^3) ).
%H A378425 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A378425 G.f.: exp( Sum_{k>=1} A378406(k) * x^k/k ).
%F A378425 a(n) = (1/(n+1)) * [x^n] (1 + x + x^2 * (1 + x)^3)^(n+1).
%F A378425 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(n+2*k+1,n-2*k).
%o A378425 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^2*(1+x)^3))/x)
%o A378425 (PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(n+2*k+1, n-2*k))/(n+1);
%Y A378425 Cf. A036765, A378426.
%Y A378425 Cf. A300048, A378427.
%Y A378425 Cf. A378406.
%K A378425 nonn
%O A378425 0,3
%A A378425 _Seiichi Manyama_, Nov 25 2024