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Search: id:A025036
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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; listen)
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OFFSET
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0,3
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COMMENT
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P-recursive - Marni Mishna (marni.mishna(AT)inria.fr), Jul 11 2005
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FORMULA
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(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
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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
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Cf. A025035, 110103, A002829.
Adjacent sequences: A025033 A025034 A025035 this_sequence A025037 A025038 A025039
Sequence in context: A001825 A094187 A115963 this_sequence A030261 A007102 A139473
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KEYWORD
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nonn,easy
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Edited by njas, Aug 23 2008 at the suggestion of R. J. Mathar
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