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A049209 a(n) = -Product_{k=0..n} (7*k-1); sept-factorial numbers. 20
1, 6, 78, 1560, 42120, 1432080, 58715280, 2818333440, 155008339200, 9610517030400, 663125675097600, 50397551307417600, 4182996758515660800, 376469708266409472000, 36517561701841718784000, 3797826416991538753536000, 421558732286060801642496000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..330

Index entries for sequences related to factorial numbers

FORMULA

a(n) = 6*A034833(n) = (7*n-1)*(!^7), n >= 1, a(0) := 1.

a(n) = Product_{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/(1-6*x/(1-7*x/(1-13*x/(1-14*x/(1-20*x/(1-21*x/(1-27*x/(1-28*x/(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

From Nikolaos Pantelidis, Dec 19 2020: (Start)

G.f.: 1/G(0) where G(k) = 1 - (14*k+6)*x - 7*(k+1)*(7*k+6)*x^2/G(k+1); (continued fraction).

which starts as 1/(1-6*x-42*x^2/(1-20*x-182*x^2/(1-34*x-420*x^2/(1-48*x-756*x^2/(1-62*x-1190*x^2/(1-... )))))) (Jacobi continued fraction).

G.f.: 1/Q(0) where Q(k) = 1 - (7*k+6)*x/(1 - (7*k+7)*x/Q(k+1) ); (continued fraction). (End)

MATHEMATICA

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

With[{m=7}, Table[m^n*Pochhammer[(m-1)/m, n], {n, 0, 30}]] (* G. C. Greubel, Feb 16 2022 *)

PROG

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

(Sage) m=7; [m^n*rising_factorial((m-1)/m, n) for n in (0..30)] # G. C. Greubel, Feb 16 2022

CROSSREFS

Cf. A034833, A045754, A051188, A084947, A144739, A144827, A147585.

Row sums of triangle A051186 (scaled Stirling1 triangle).

Sequences of the form m^n*Pochhammer((m-1)/m, n): A000007 (m=1), A001147 (m=2), A008544 (m=3), A008545 (m=4), A008546 (m=5), A008543 (m=6), this sequence (m=7), A049210 (m=8), A049211 (m=9), A049212 (m=10), A254322 (m=11), A346896 (m=12).

Sequence in context: A094419 A229044 A300874 * A162656 A332680 A179498

Adjacent sequences:  A049206 A049207 A049208 * A049210 A049211 A049212

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)