A220747 a(n) = (2*n+1)!! / ((floor((n-1)/3)*2+1))!!

1, 3, 15, 105, 315, 3465, 45045, 135135, 2297295, 43648605, 130945815, 3011753745, 75293843625, 225881530875, 6550564395375, 203067496256625, 609202488769875, 21322087106945625, 788917222956988125

Offset

0,2

Comments

The a(n) appear in the analysis of a sequence that is related to the Madhava-Gregory-Leibniz formula for Pi, see A166107.

Links

Table of n, a(n) for n=0..18.

Formula

Limit_{n -> infinity} A166107(2*n)/a(2*n) = Pi.

Limit_{n -> infinity} A166107(2*n+1)/a(2*n+1) = -Pi.

E.g.f.: 2F2(5/6,7/6; 1/3,2/3; 4*x^3) + 3*x*(2F2(5/6,7/6; 2/3,4/3; 4*x^3) + 5*x*2F2(7/6,11/6; 4/3,5/3; 4*x^3)/2). - Benedict W. J. Irwin, Oct 19 2016

Maple

A220747 := n -> doublefactorial(2*n+1)/doublefactorial(A130823(n)): A130823 := n -> floor((n-1)/3)*2+1: seq(A220747(n), n=0..20);

Mathematica

Table[(2*n + 1)!!/((Floor[(n - 1)/3]*2 + 1))!!, {n, 0, 20}] (* T. D. Noe, Feb 26 2013 *)
CoefficientList[Series[HypergeometricPFQ[{5/6, 7/6}, {1/3, 2/3}, 4 x^3] + 3/2 x (2 HypergeometricPFQ[{5/6, 7/6}, {2/3, 4/3}, 4 x^3] + 5x HypergeometricPFQ[{7/6, 11/6}, {4/3, 5/3}, 4 x^3]), {x, 0, 20}], x]*Range[0, 20]! (* Benedict W. J. Irwin, Oct 19 2016 *)

Crossrefs

Cf. A000796, A001147, A130823, A166107.

Sequence in context: A025547 A352395 A350670 * A088989 A001801 A323551

Adjacent sequences: A220744 A220745 A220746 * A220748 A220749 A220750

Keyword

nonn,easy

Author

Johannes W. Meijer, Feb 26 2013

Status

approved