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 A047055 Quintuple factorial numbers: product_{ k=0..n-1 } (5*k+2). 16
 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. [From Paul Barry, Dec 03 2009] LINKS FORMULA E.g.f. (1-5*x)^(-2/5) a(n) ~ 2^(1/2)*pi^(1/2)*Gamma(2/5)^-1*n^(-1/10)*5^n*e^-n*n^n*{1 - 11/300*n^-1 - ...}. - 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). [From 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. [From 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 [From Vladimir Joseph Stephan Orlovsky, Nov 08 2008] CROSSREFS Cf. A000165, A008544, A001813, A047657, A084947, A084948, A084949. Cf. A052562, A008548, A047056. Sequence in context: A124215 A003582 A084946 * A188194 A046247 A141012 Adjacent sequences:  A047052 A047053 A047054 * A047056 A047057 A047058 KEYWORD nonn,easy AUTHOR Joe Keane (jgk(AT)jgk.org) STATUS approved

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