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A049209 a(n) = -product_{k=0..n} (7*k-1); sept-factorial numbers. 16
1, 6, 78, 1560, 42120, 1432080, 58715280, 2818333440, 155008339200, 9610517030400, 663125675097600, 50397551307417600, 4182996758515660800, 376469708266409472000, 36517561701841718784000 (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) = 6*A034883(n) = (7*n-1)(!^7), n >= 1, a(0) := 1.

a(n) = Prod_{k=1..n} (7*k - 1). a(0) = 1; a(n) = (7*n - 1)*a(n-1) for n > 0. - Klaus Brockhaus, Nov 10 2008

G.f.: 1/(1-6x/(1-7x/(1-13x/(1-14x/(1-20x/(1-21x/(1-27x/(1-28x/(1-...(continued fraction). - Philippe Deléham, Jan 08 2012

a(n) = (-1)^n*sum_{k=0..n} 7^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

a(n) = 7^n * GAMMA(n+6/7) / GAMMA(6/7). - Vaclav Kotesovec, Jan 28 2015

E.g.f: (1-7*x)^(-6/7). - Vaclav Kotesovec, Jan 28 2015

MATHEMATICA

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 5, 5!, 7}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)

CoefficientList[Series[(1-7*x)^(-6/7), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 28 2015 *)

PROG

(MAGMA) [ -&*[ (7*k-1): k in [0..n-1] ]: n in [1..15] ]; // Klaus Brockhaus, Nov 10 2008

CROSSREFS

Cf. A008543.

Row sums of triangle A051186 (scaled Stirling1 triangle).

Cf. A045754, A084947, A144739, A144827, A147585, A051188.

Sequence in context: A094419 A229044 A300874 * A162656 A179498 A177556

Adjacent sequences:  A049206 A049207 A049208 * A049210 A049211 A049212

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)