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A132912 a(n)=C(n+2,2)(2n)!/2^n. 1
1, 3, 36, 900, 37800, 2381400, 209563200, 24518894400, 3677834160000, 687754987920000, 156808137245760000, 42808621468092480000, 13784376112725778560000, 5169141042272166960000000, 2233068930261576126720000000, 1100902982618957030472960000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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^(2j)/2^j}. T(n,1) is A000680 with interpolated zeros. T(n,2) is A132911.

LINKS

Table of n, a(n) for n=0..15.

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A326273 A224006 A004824 * A303866 A126447 A102921

Adjacent sequences:  A132909 A132910 A132911 * A132913 A132914 A132915

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 04 2007

EXTENSIONS

More terms from Harvey P. Dale, Sep 18 2011

STATUS

approved

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Last modified October 24 10:40 EDT 2021. Contains 348225 sequences. (Running on oeis4.)