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A049210 a(n) = -product_{k=0..n} (8*k-1); octo-factorial numbers. 6
1, 7, 105, 2415, 74865, 2919735, 137227545, 7547514975, 475493443425, 33760034483175, 2667042724170825, 232032717002861775, 22043108115271868625, 2270440135873002468375, 252018855081903273989625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for sequences related to factorial numbers

FORMULA

a(n) = 7*A034975(n) = (8*n-1)(!^8), n >= 1, a(0) = 1.

G.f.: 1/(1-7x/(1-8x/(1-15x/(1-16x/(1-23x/(1-24x/(1-31x/(1-32x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012

a(n) = (-1)^n*sum_{k=0..n} 8^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 - 1/Q(0) )/x where Q(k) = 1 - x*(8*k-1)/(1 - x*(8*k+8)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 20 2013

a(n) = 8^n*Gamma(n+7/8)/Gamma(7/8). - R. J. Mathar, Mar 20 2013

E.g.f: (1-8*x)^(-7/8). - Vaclav Kotesovec, Jan 28 2015

MATHEMATICA

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 6, 5!, 8}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)

FoldList[Times, 1, 8*Range[20]-1] (* Harvey P. Dale, Aug 03 2014 *)

CoefficientList[Series[(1-8*x)^(-7/8), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 28 2015 *)

PROG

(PARI) a(n) = -prod(k=0, n, 8*k-1); \\ Michel Marcus, Jan 08 2015

CROSSREFS

Cf. A008543, A049209, A049211, A049212, A051187.

Sequence in context: A145666 A238464 A096131 * A167814 A209545 A002486

Adjacent sequences:  A049207 A049208 A049209 * A049211 A049212 A049213

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified February 17 14:12 EST 2018. Contains 299296 sequences. (Running on oeis4.)