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

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

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^(2*j)/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

From Amiram Eldar, Jan 04 2026: (Start)

Sum_{n>=0} 1/a(n) = 2^(7/4)*sqrt(Pi)*BesselI(-5/2, sqrt(2)) - 4.

Sum_{n>=0} (-1)^n/a(n) = 6*sqrt(2)*sin(sqrt(2)) + 2*cos(sqrt(2)) - 8. (End)

Mathematica

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

Crossrefs

Cf. A000680, A132911.

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