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A025036
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Number of partitions of { 1, 2, ..., 4n } into sets of size 4.
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3
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1, 1, 35, 5775, 2627625, 2546168625, 4509264634875, 13189599057009375, 59287247761257140625, 388035036597427985390625, 3546252199463894358484921875, 43764298393583920278062420859375
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| P-recursive - Marni Mishna (marni.mishna(AT)inria.fr), Jul 11 2005
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FORMULA
| (4n)!/(n!(4!)^n). (Christian G. Bower bowerc(AT)usa.net Sep 15 1998).
E.g.f. A(t)=sum a(n)t^(4n)/(4n!) = exp(t^4/4!); recurrence: (3+22*n+48*n^2+32*n^3)*a(n)-3*a(n+1) - Marni Mishna (marni.mishna(AT)inria.fr), Jul 11 2005
Integral representation as n-th moment of a positive function on the positive axis in Maple notation: a(n)=int(x^n*(1/4*(2^(3/4)*hypergeom([], [5/4, 3/2], -3/32*x)*3^(3/4)*GAMMA(3/4)^2*x*Pi^(1/2)-2*hypergeom([], [3/4, 5/4], -3/32*x)*3^(1/2)*2^(1/2)*Pi*x^(3/4)*GAMMA(3/4)+hypergeom([], [1/2, 3/4], -3/32*x)*3^(1/4)*2^(3/4)*Pi^(3/2)*x^(1/2))/Pi^(3/2)/x^(5/4)/GAMMA(3/4)), x=0..infinity), n=0, 1..., with offset 1. -Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 6 2005.
E.g.f.: exp(x^4/4!) (with interpolated zeros) - Paul Barry (pbarry(AT)wit.ie), May 26 2003
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EXAMPLE
| a(1)=1: {1,2,3,4}
One of the a(2)=35 partitions for n = 8: {1,2,3,4}{5,6,7,8}
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CROSSREFS
| Cf. A025035, 110103, A002829.
Sequence in context: A115963 A202067 A202881 * A202066 A030261 A007102
Adjacent sequences: A025033 A025034 A025035 * A025037 A025038 A025039
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KEYWORD
| nonn,easy
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2008 at the suggestion of R. J. Mathar
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