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A006200
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Number of partitions into pairs.
(Formerly M4263)
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1
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1, 6, 55, 610, 7980, 120274, 2052309, 39110490, 823324755, 18974858540, 475182478056, 12848667150956, 373081590628565, 11578264139795430, 382452947343624515, 13397354334102974934, 496082324933446766724, 19360538560004548357830, 794275868644522931369185
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OFFSET
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1,2
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REFERENCES
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G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonne, Publications de l'Institut de Statistique de l'Université de Paris, 23 (1978), 57-74.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) ~ 2^(n + 3/2) * n^(n + 2) / (3 * exp(n + 1)). - Vaclav Kotesovec, May 20 2018
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MAPLE
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a:= proc(n) option remember; `if`(n<2, n,
(n*(4*n^2-7)*a(n-1)+(n+1)*(2*n+1)*a(n-2))/((2*n-1)*(n-1)))
end:
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MATHEMATICA
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Table[(2*n+1)! * Hypergeometric1F1[1-n, -1-2*n, -2] / (3*2^n*(n-1)!), {n, 1, 20}] (* Vaclav Kotesovec, Jan 24 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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