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A047657 Sextuple factorial numbers: a(n) = Product_{k=0..n-1} (6*k+2). 17
1, 2, 16, 224, 4480, 116480, 3727360, 141639680, 6232145920, 311607296000, 17450008576000, 1081900531712000, 73569236156416000, 5444123475574784000, 435529878045982720000, 37455569511954513920000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

E.g.f.: (1-6*x)^(-1/3).

a(n) = 2^n*A007559(n).

a(n) = A084941(n)/A000142(n)*A000079(n) = 6^n*pochhammer(1/3, n) = 1/2*6^n*GAMMA(n+1/3)*sqrt(3)*GAMMA(2/3)/Pi. - Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003

Let b(n) = b(n-1) + 6; then a(n) = b(n)*a(n-1). - Roger L. Bagula, Sep 17 2008

G.f.: 1/(1-2x/(1-6x/(1-8x/(1-12x/(1-14x/(1-18x/(1-20x/(1-24x/(1-26x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012

a(n) = (-4)^n*sum_{k=0..n} (3/2)^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.: 1/G(0) where G(k) = 1 - x*(6*k+2)/( 1 - 6*x*(k+1)/G(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 23 2013

MATHEMATICA

k = 6; b[1] = 2; b[n_] := b[n] = b[n - 1] + k; a[0] = 1; a[1] = 2; a[n_] := a[n] = a[n - 1]*b[n]; Table[a[n], {n, 0, 20}] (* Roger L. Bagula, Sep 17 2008 *)

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 1, 5!, 6}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)

FoldList[Times, 1, 6*Range[0, 20]+2] (* Harvey P. Dale, Aug 06 2013 *)

CROSSREFS

Cf. A007559, A008542, A011781.

Cf. A000165, A008544, A001813, A047055, A084947, A084948, A084949.

Sequence in context: A188688 A188844 A187657 * A233141 A223631 A188500

Adjacent sequences:  A047654 A047655 A047656 * A047658 A047659 A047660

KEYWORD

nonn,easy

AUTHOR

Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified October 23 18:48 EDT 2018. Contains 316530 sequences. (Running on oeis4.)