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A081668
Expansion of 2sinh(x) + BesselI_0(2x).
2
1, 2, 2, 2, 6, 2, 20, 2, 70, 2, 252, 2, 924, 2, 3432, 2, 12870, 2, 48620, 2, 184756, 2, 705432, 2, 2704156, 2, 10400600, 2, 40116600, 2, 155117520, 2, 601080390, 2, 2333606220, 2, 9075135300, 2, 35345263800, 2, 137846528820, 2, 538257874440, 2
OFFSET
0,2
COMMENTS
Binomial transform of A081668 is A081669.
a(n)-(1-(-1)^n) is the inverse binomial transform of the central trinomial coefficients A002426. - N-E. Fahssi, Jan 11 2008
LINKS
FORMULA
E.g.f. 2sinh(x) + BesselI_0(2x)
G.f.: (2x)/(1 - x^2) + 1/Sqrt[1 - 4 x^2]. - N-E. Fahssi, Jan 11 2008
If n is even, a(n) ~ 2^(n+1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Feb 12 2014
MATHEMATICA
CoefficientList[Series[2*Sinh[x] + BesselI[0, 2*x], {x, 0, 20}], x]*Range[0, 20]! (* Vaclav Kotesovec, Feb 12 2014 *)
CROSSREFS
Cf. A000984 (bisection).
Sequence in context: A078020 A339091 A097521 * A126615 A158524 A054274
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 28 2003
STATUS
approved