%I A047055
%S A047055 1,2,14,168,2856,62832,1696464,54286848,2008613376,84361761792,
%T A047055 3965002804224,206180145819648,11752268311719936,728640635326636032,
%U A047055 48818922566884614144,3514962424815692218368,270652106710808300814336
%N A047055 Quintuple factorial numbers: product_{ k=0..n-1 } (5*k+2).
%C A047055 Hankel transform is A169621. [From Paul Barry (pbarry(AT)wit.ie), Dec 
               03 2009]
%F A047055 E.g.f. (1-5*x)^(-2/5)
%F A047055 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
%F A047055 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
%F A047055 Let b(n)=b(n-1)+5; then a(n)=b(n)*a(n-1). - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), 
               Sep 17 2008
%F A047055 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 (pbarry(AT)wit.ie), Dec 03 2009]
%p A047055 a := n->product(5*i+2,i=0..n-1); [seq(a(j),j=0..30)];
%t A047055 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 
               (rlbagulatftn(AT)yahoo.com), Sep 17 2008
%t A047055 s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 1, 5!, 5}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
%Y A047055 Cf. A000165, A008544, A001813, A047657, A084947, A084948, A084949.
%Y A047055 Cf. A052562, A008548, A047056.
%Y A047055 Sequence in context: A124215 A003582 A084946 this_sequence A046247 A141012 
               A167014
%Y A047055 Adjacent sequences: A047052 A047053 A047054 this_sequence A047056 A047057 
               A047058
%K A047055 nonn,easy,new
%O A047055 0,2
%A A047055 Joe Keane (jgk(AT)jgk.org)