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A144756 Partial products of successive terms of A017101; a(0)=1 . 3
1, 3, 33, 627, 16929, 592515, 25478145, 1299385395, 76663738305, 5136470466435, 385235284982625, 31974528653557875, 2909682107473766625, 288058528639902895875, 30822262564469609858625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

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)

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

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 2, 5!, 8}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)

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

CROSSREFS

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

Sequence in context: A083080 A002916 A009659 * A336636 A326328 A233319

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

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Last modified August 5 19:30 EDT 2020. Contains 336213 sequences. (Running on oeis4.)