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A132911
a(n) = (n+1)*(2*n)!/2^n.
1
1, 2, 18, 360, 12600, 680400, 52390800, 5448643200, 735566832000, 125046361440000, 26134689540960000, 6585941764321920000, 1969196587532254080000, 689218805636288928000000, 279133616282697015840000000, 129517997955171415349760000000, 68255984922375335889323520000000
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,3) is A132912.
LINKS
Daniele Marchei, Emanuela Merelli, and Andrew Francis, Factorizing the Brauer monoid in polynomial time, arXiv:2402.07874 [math.RA], 2024. See p. 24.
FORMULA
E.g.f.: 1/(1-x^2+x^4/4) (with interpolated zeros);
a(n)-(n+1)*(2*n-1)*a(n-1)=0. - R. J. Mathar, Nov 05 2012
MATHEMATICA
Table[(n+1) (2n)!/2^n, {n, 0, 20}] (* Harvey P. Dale, Jun 02 2020 *)
CROSSREFS
Sequence in context: A123311 A349881 A181536 * A291902 A336217 A226837
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 04 2007
STATUS
approved