cp's OEIS Frontend

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.

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A132912 a(n) = C(n+2,2)*(2*n)!/2^n.

Original entry on oeis.org

1, 3, 36, 900, 37800, 2381400, 209563200, 24518894400, 3677834160000, 687754987920000, 156808137245760000, 42808621468092480000, 13784376112725778560000, 5169141042272166960000000, 2233068930261576126720000000, 1100902982618957030472960000000
Offset: 0

Views

Author

Paul Barry, Sep 04 2007

Keywords

Comments

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.

Crossrefs

Cf. A000680, A132911.

Programs

  • Mathematica
    Table[(Binomial[n+2,2](2n)!)/2^n,{n,0,20}] (* Harvey P. Dale, Sep 18 2011 *)

Formula

E.g.f.: 1/(1-(3/2)*x^2+(3/4)*x^4-(1/8)*x^6) (with interpolated zeros).
a(n) -(n+2)*(2*n-1)*a(n-1)=0. - R. J. Mathar, Nov 05 2012

Extensions

More terms from Harvey P. Dale, Sep 18 2011
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