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A008543 Sextuple factorial numbers: Product_{k=0..n-1} (6*k + 5). 23
1, 5, 55, 935, 21505, 623645, 21827575, 894930575, 42061737025, 2229272062325, 131527051677175, 8549258359016375, 606997343490162625, 46738795448742522125, 3879320022245629336375, 345259481979861010937375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

FORMULA

a(n) = 5*A034787(n) = (6*n-1)(!^6), n >= 1, a(0) := 1.

E.g.f.: (1 - 6*x)^(-5/6).

a(n) ~ 2^(1/2)*Pi^(1/2)*Gamma(5/6)^-1*n^(1/3)*6^n*e^-n*n^n*{1 + (1/72)*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

G.f.: 1/(1-5x/(1-6x/(1-11x/(1-12x/(1-17x/(1-18x/(1-23x/(1-24x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012

a(n) = (-1)^n*Sum_{k=0..n} 6^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*(6*k-1)/(1 - x*(6*k+6)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Mar 20 2013

a(n) = 6^n * Gamma(n+5/6) / Gamma(5/6). - Vaclav Kotesovec, Jan 28 2015

D-finite with recurrence: a(n) +(-6*n+1)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

MAPLE

f := n->product( (6*k-1), k=0..n);

MATHEMATICA

FoldList[Times, 1, 6Range[0, 15]+5]  (* Harvey P. Dale, Feb 20 2011 *)

Table[6^n*Pochhammer[5/6, n], {n, 0, 20}] (* G. C. Greubel, Dec 03 2019 *)

PROG

(PARI) a(n)=prod(k=1, n, 6*k-1) \\ Charles R Greathouse IV, Aug 17 2011

(MAGMA) [Round(6^n*Gamma(n+5/6)/Gamma(5/6)): n in [0..20]]; // G. C. Greubel, Dec 03 2019

(Sage) [6^n*rising_factorial(5/6, n) for n in (0..20)] # G. C. Greubel, Dec 03 2019

CROSSREFS

a(n) = A013988(n+1, 1) (first column of triangle).

Cf. A004994, A034787, A049308, A047058, A048994, A051151.

Sequence in context: A294051 A145662 A094418 * A057130 A141357 A093352

Adjacent sequences:  A008540 A008541 A008542 * A008544 A008545 A008546

KEYWORD

nonn,easy

AUTHOR

Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified February 26 11:49 EST 2020. Contains 332279 sequences. (Running on oeis4.)