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A047055
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Quintuple factorial numbers: product_{ k=0..n-1 } (5*k+2).
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16
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1, 2, 14, 168, 2856, 62832, 1696464, 54286848, 2008613376, 84361761792, 3965002804224, 206180145819648, 11752268311719936, 728640635326636032, 48818922566884614144, 3514962424815692218368, 270652106710808300814336
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is A169621. [From Paul Barry (pbarry(AT)wit.ie), Dec 03 2009]
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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 (rlbagulatftn(AT)yahoo.com), 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 (pbarry(AT)wit.ie), Dec 03 2009]
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MAPLE
| a := n->product(5*i+2, i=0..n-1); [seq(a(j), j=0..30)];
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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 (rlbagulatftn(AT)yahoo.com), Sep 17 2008
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]
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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
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KEYWORD
| nonn,easy
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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