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 A378426 #11 Nov 26 2024 09:32:25
%S A378426 1,1,2,6,18,56,184,624,2161,7621,27283,98869,361967,1336843,4974763,
%T A378426 18634683,70207751,265874119,1011475368,3863846328,14814818017,
%U A378426 56994831109,219941836172,851138940402,3302281633591,12842844277471,50056915575566,195503017533502
%N A378426 Expansion of (1/x) * Series_Reversion( x / (1 + x + x^2 * (1 + x)^2) ).
%H A378426 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A378426 G.f.: exp( Sum_{k>=1} A378405(k) * x^k/k ).
%F A378426 a(n) = (1/(n+1)) * [x^n] (1 + x + x^2 * (1 + x)^2)^(n+1).
%F A378426 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(n+k+1,n-2*k).
%o A378426 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^2*(1+x)^2))/x)
%o A378426 (PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(n+k+1, n-2*k))/(n+1);
%Y A378426 Cf. A036765, A378425.
%Y A378426 Cf. A378405.
%K A378426 nonn
%O A378426 0,3
%A A378426 _Seiichi Manyama_, Nov 25 2024