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A007820
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Stirling numbers of second kind S(2n,n).
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11
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1, 7, 90, 1701, 42525, 1323652, 49329280, 2141764053, 106175395755, 5917584964655, 366282500870286, 24930204590758260, 1850568574253550060, 148782988064375309400, 12879868072770626040000, 1194461517469807833782085, 118144018577011378596484455
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 835.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..49
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
O-Y. Chan and D. V. Manna, Divisibility properties of Stirling numbers of the second kind [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Sep 14 2009]
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FORMULA
| a(n) = A048993(2n,n). - R. J. Mathar, Mar 15 2011
Asymptotic: a(n) ~ (4*n/(e*z*(2-z)))^n/sqrt(2*pi*n*(z-1)), where z=1.59362426... is a root of the equation exp(z)*(2-z)=2. [Vaclav Kotesovec, May 30 2011]
a(n) = sum(binomial(n,k)*(-1)^k*(n-k)^(2*n),k,0,n)/n! [Emanuele Munarini, Jul 1 2011]
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MAPLE
| A007820 := proc(n) combinat[stirling2](2*n, n) ; end proc:
seq(A007820(n), n=1..20) ; # R. J. Mathar, Mar 15 2011
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MATHEMATICA
| Table[StirlingS2[2n, n], {n, 0, 12}] (* Emanuele Munarini, Mar 12 2011*)
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PROG
| (Sage) [stirling_number2(2*i, i) for i in xrange(1, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 26 2008
(Maxima) makelist(stirling2(2*n, n), n, 0, 12); /* Emanuele Munarini, Mar 12 2011 */
(PARI) a(n)=stirling(2*n, n, 2); /* Joerg Arndt, Jul 01 2011 */
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CROSSREFS
| Chan and Manna prove that a(n) is odd if and only if n is in A003714. [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Sep 14 2009]
Cf. A187646, A002465, A191236
Sequence in context: A142995 A200832 A103064 * A123694 A085026 A181475
Adjacent sequences: A007817 A007818 A007819 * A007821 A007822 A007823
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KEYWORD
| nonn,easy
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AUTHOR
| kemp(AT)sads.informatik.uni-frankfurt.de (Rainer Kemp)
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