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 A381817 #11 Mar 10 2025 11:02:14
%S A381817 1,2,8,41,239,1507,10016,69123,490676,3560150,26285896,196862679,
%T A381817 1491921261,11420072162,88166571504,685724643699,5367842153463,
%U A381817 42259058503891,334373741310812,2657683458672907,21209720057079565,169886023881795700,1365290865904393560
%N A381817 Expansion of (1/x) * Series_Reversion( x * (1-x) / C(x) ), where C(x) is the g.f. of A000108.
%F A381817 G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x*A(x)).
%F A381817 a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(2*n-k,n-k)/(n+2*k+1).
%F A381817 D-finite with recurrence 270*n*(n-1)*(2*n+1)*(4886806261*n -12359738163)*(n+1)*a(n) +36*n*(n-1)*(73302093915*n^3 -4013759132354*n^2 +11228589268975*n -4731576382254)*a(n-1) -6*(n-1)*(78948725805818*n^4 -721014042837927*n^3 +2114039183987386*n^2 -2373558292742247*n +834825525358878)*a(n-2) +(3703469060597227*n^5 -40768871113864973*n^4 +173554734639707111*n^3 -360669855974794759*n^2 +370762762031723274*n -153683482287306096)*a(n-3) +6*(-2284895393144753*n^5 +28245013068548213*n^4 -138588666805096327*n^3 +341806596235129383*n^2 -433338949590369664*n +232825263110939100)*a(n-4) +10*(5*n-22)*(5*n-21) *(5*n-19)*(5*n-18)*(1032930487477*n -4077934418263)*a(n-5)=0. - _R. J. Mathar_, Mar 10 2025
%o A381817 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*2*x/(1-sqrt(1-4*x)))/x)
%Y A381817 Cf. A381818, A381819, A381820.
%Y A381817 Cf. A000108.
%K A381817 nonn
%O A381817 0,2
%A A381817 _Seiichi Manyama_, Mar 07 2025