A081668 Expansion of 2sinh(x) + BesselI_0(2x).

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A081665 A081666 A081667 * A081669 A081670 A081671

Keyword

easy,nonn

Author

Paul Barry, Mar 28 2003

Status

approved