A144756 Partial products of successive terms of A017101; a(0)=1 .

1, 3, 33, 627, 16929, 592515, 25478145, 1299385395, 76663738305, 5136470466435, 385235284982625, 31974528653557875, 2909682107473766625, 288058528639902895875, 30822262564469609858625, 3544560194914005133741875, 435980903974422631450250625, 57113498420649364719982831875

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} A132393(n,k)*3^k*8^(n-k).

a(n) = (-5)^n*sum_{k=0..n} (8/5)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012

G.f.: 2/G(0), where G(k)= 1 + 1/(1 - 2*x*(8*k+3)/(2*x*(8*k+3) - 1 + 16*x*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 30 2013

a(n) +(-8*n+5)*a(n-1)=0. - R. J. Mathar, Sep 04 2016

From Ilya Gutkovskiy, Mar 23 2017: (Start)

E.g.f.: 1/(1 - 8*x)^(3/8).

a(n) ~ sqrt(2*Pi)*8^n*n^n/(exp(n)*n^(1/8)*Gamma(3/8)). (End)

Sum_{n>=0} 1/a(n) = 1 + (e/8^5)^(1/8)*(Gamma(3/8) - Gamma(3/8, 1/8)). - Amiram Eldar, Dec 20 2022

Example

a(0)=1, a(1)=3, a(2)=3*11=33, a(3)=3*11*19=627, a(4)=3*11*19*27=16929, ...

Mathematica

Join[{1}, FoldList[Times, 8Range[0, 20]+3]] (* Harvey P. Dale, Aug 11 2019 *)

Crossrefs

Cf. A001710, A001147, A008545, A011781, A017101, A032031, A047056, A048994, A144739.

Sequence in context: A009659 A367427 A361212 * A377453 A377446 A336636

Adjacent sequences: A144753 A144754 A144755 * A144757 A144758 A144759

Keyword

nonn,easy

Author

Philippe Deléham, Sep 20 2008

Extensions

a(11) corrected by Ilya Gutkovskiy, Mar 23 2017

Status

approved