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 A132912 #11 Aug 31 2025 18:30:04
%S A132912 1,3,36,900,37800,2381400,209563200,24518894400,3677834160000,
%T A132912 687754987920000,156808137245760000,42808621468092480000,
%U A132912 13784376112725778560000,5169141042272166960000000,2233068930261576126720000000,1100902982618957030472960000000
%N A132912 a(n) = C(n+2,2)*(2*n)!/2^n.
%C A132912 Define T(n,k) = ((1+(-1)^n)/2)*C(k-1+n/2, n/2)*n!/2^(n/2). Then T(n,k) has e.g.f. 1/(Sum_{j=0..k} C(k,j)*(-1)^j*x^(2*j)/2^j). T(n,1) is A000680 with interpolated zeros. T(n,2) is A132911.
%F A132912 E.g.f.: 1/(1-(3/2)*x^2+(3/4)*x^4-(1/8)*x^6) (with interpolated zeros).
%F A132912 a(n) -(n+2)*(2*n-1)*a(n-1)=0. - _R. J. Mathar_, Nov 05 2012
%t A132912 Table[(Binomial[n+2,2](2n)!)/2^n,{n,0,20}] (* _Harvey P. Dale_, Sep 18 2011 *)
%Y A132912 Cf. A000680, A132911.
%K A132912 easy,nonn,changed
%O A132912 0,2
%A A132912 _Paul Barry_, Sep 04 2007
%E A132912 More terms from _Harvey P. Dale_, Sep 18 2011