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A034176
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One third of quartic factorial numbers.
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15
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1, 7, 77, 1155, 21945, 504735, 13627845, 422463195, 14786211825, 576662261175, 24796477230525, 1165434429834675, 59437155921568425, 3269043575686263375, 192873570965489539125, 12151034970825840964875
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| 3*a(n) = (4*n-1)(!^4) := product(4*j-1, j=1..n) = (4*n-1)!!/A007696(n) = (4*n)!/(4^n*(2*n)!*A007696(n)), A007696(n)=(4*n-3)(!^4), n >= 1; E.g.f. (-1+(1-4*x)^(-3/4))/3.
a(n) ~ 4/3*2^(1/2)*pi^(1/2)*Gamma(3/4)^-1*n^(5/4)*2^(2*n)*e^-n*n^n*{1 + 71/96*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 23 2001
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MATHEMATICA
| s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 6, 5!, 4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
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CROSSREFS
| Cf. A007696, A034177, A034256, A025749.
Sequence in context: A002281 A097983 A107866 * A001765 A093980 A077706
Adjacent sequences: A034173 A034174 A034175 * A034177 A034178 A034179
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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