A098461 Expansion of E.g.f.: 1/sqrt(1-2*x-3*x^2).
1, 1, 6, 42, 456, 6120, 101520, 1980720, 44634240, 1139080320, 32488646400, 1023985670400, 35345049062400, 1325988036172800, 53721616851302400, 2337607853957376000, 108727934847307776000, 5383304681800421376000, 282682783375630589952000
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..379
Programs
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Mathematica
Table[(n!/2^n) Sum[Binomial[n, k] Binomial[2 (n - k), n] 3^k, {k, 0, Floor[n/2]}], {n, 0, 17}] (* Michael De Vlieger, Sep 14 2016 *)
Formula
a(n) = (n!/2^n)*A098453(n);
a(n) = (n!/2^n)*Sum_{k=0..floor(n/2)} binomial(n, k)*binomial(2*(n-k), n)*3^k.
D-finite with recurrence: a(n) +(1-2n)*a(n-1) -3(n-1)^2*a(n-2)=0. - R. J. Mathar, Dec 11 2011
a(n) = n! * A002426(n). - Anton Zakharov, Sep 14 2016