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A008546 Quintuple factorial numbers: Product_{k=0..n-1} (5*k+4). 26
1, 4, 36, 504, 9576, 229824, 6664896, 226606464, 8837652096, 388856692224, 19053977918976, 1028914807624704, 60705973649857536, 3885182313590882304, 268077579637770878976, 19837740893195045044224 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

FORMULA

a(n) = 4*A034301(n) = (5*n-1)(!^5), n >= 1, a(0) := 1.

a(n) ~ 2^(1/2)*Pi^(1/2)*Gamma(4/5)^-1*n^(3/10)*5^n*e^-n*n^n*{1 + 1/300*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

G.f.: 1/(1-4x/(1-5x/(1-9x/(1-10x/(1-14x/(1-15x/(1-19x/(1-20x/(1-24x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012

a(n) = (-1)^n*sum_{k=0..n} 5^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*(5*k-1)/(1 - x*(5*k+5)/Q(k+1) ); (continued fraction); E.g.f. (1-5*x)^(-4/5). - Sergei N. Gladkovskii, Mar 20 2013

G.f.: 1/x - G(0)/(2*x), where G(k)= 1 + 1/(1 - x*(5*k-1)/(x*(5*k-1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 27 2013

a(n) = 5^n * GAMMA(n+4/5) / GAMMA(4/5). - Vaclav Kotesovec, Jan 28 2015

a(n) +(-5*n+1)*a(n-1)=0. - R. J. Mathar, Sep 04 2016

MAPLE

f := n->product( (5*k-1), k=0..n);

MATHEMATICA

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 3, 5!, 5}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)

FoldList[Times, 1, 5Range[0, 20] + 4] (* Vincenzo Librandi, Jun 10 2013 *)

CoefficientList[Series[(1-5*x)^(-4/5), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 28 2015 *)

CROSSREFS

a(n)= A011801(n+1, 1) (first column of triangle).

Cf. A008548, A047056, A047055, A052562, A051150, A052562, A254287.

Sequence in context: A002690 A094417 A138435 * A277404 A024253 A052746

Adjacent sequences:  A008543 A008544 A008545 * A008547 A008548 A008549

KEYWORD

nonn

AUTHOR

Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified February 21 16:28 EST 2018. Contains 299414 sequences. (Running on oeis4.)