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A047055 Quintuple factorial numbers: a(n) = product_{k=0..n-1} (5*k + 2). 24
1, 2, 14, 168, 2856, 62832, 1696464, 54286848, 2008613376, 84361761792, 3965002804224, 206180145819648, 11752268311719936, 728640635326636032, 48818922566884614144, 3514962424815692218368, 270652106710808300814336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A169621. - Paul Barry, Dec 03 2009

LINKS

Table of n, a(n) for n=0..16.

FORMULA

E.g.f. (1-5*x)^(-2/5).

a(n) ~ sqrt(2*Pi)/Gamma(2/5)*n^(-1/10)*(5n/e)^n*(1 - (11/300)/n - ...). - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

a(n) = A084940(n)/A000142(n)*A000079(n) = 5^n*pochhammer(2/5, n) = 5^n*GAMMA(n+2/5)*sin(2*Pi/5)*GAMMA(3/5)/Pi. - Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003

Let b(n) = b(n-1) + 5; then a(n) = b(n)*a(n-1). - Roger L. Bagula, Sep 17 2008

G.f.: 1/(1-2x/(1-5x/(1-7x/(1-10x/(1-12x/(1-15x/(1-17x/(1-20x/(1-22x/(1-25x/(1-.../(1-A047215(n+1)*x/(1-... (continued fraction). - Paul Barry, Dec 03 2009

a(n) = (-3)^n*sum_{k=0..n} (5/3)^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) +(-5*n+3)*a(n-1) = 0. - R. J. Mathar, Dec 03 2012

G.f.: 1/G(0) where G(k) = 1 - x*(5*k+2)/( 1 - 5*x*(k+1)/G(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 23 2013

MAPLE

a := n->product(5*i+2, i=0..n-1); [seq(a(j), j=0..30)];

MATHEMATICA

k = 5; b[1] = 2; b[n_] := b[n] = b[n - 1] + k; a[0] = 1; a[1] = 2; a[n_] := a[n] = a[n - 1]*b[n]; Table[a[n], {n, 0, 20}] (* Roger L. Bagula, Sep 17 2008 *)

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

CROSSREFS

Cf. A000165, A008544, A001813, A047657, A084947, A084948, A084949.

Cf. A052562, A008548, A047056.

Sequence in context: A003582 A277373 A084946 * A229257 A188194 A046247

Adjacent sequences:  A047052 A047053 A047054 * A047056 A047057 A047058

KEYWORD

nonn,easy

AUTHOR

Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)