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A028353
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Coefficient of x^(2*n+1) in arctanh(x)/sqrt(1-x^2), multiplied by (2*n+1)!.
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2
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1, 5, 89, 3429, 230481, 23941125, 3555578025, 715154761125, 187188449198625, 61836509511685125, 25163273966324405625, 12368068140988819153125, 7224011282550809645600625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of degree-(2*n+1) permutations with exactly one odd cycle. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 13 2004
a(n)=sum over all multinomials M2(2*n+1,k), k from {1..p(2*n+1)} restricted to partitions with exactly one odd and possibly even parts. p(2*n+1)= A000041(2*n+1) (partition numbers) and for the M2-multinomial numbers in A-St order see A036039(2*n+1,k). W. Lang, Aug 07 2007.
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EXAMPLE
| arctanh(x)/sqrt(1-x^2) = x + 5/6*x^3 + 89/120*x^5 + 381/560*x^7 + ...
Multinomial representation for a(2): partitions of 2*2+1=5 with one odd part: (5) with position k=1, (1,4) with k=2, (2,3) with k=3, (1,2^2) with k=5; M2(5,1)= 24, M2(5,2)= 30, M2(5,3)= 20, M2(5,5)= 15, adding up to a(2)=89.
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CROSSREFS
| Cf. A060338.
Cf. A060524.
Sequence in context: A167735 A067257 A134497 * A191512 A015085 A067258
Adjacent sequences: A028350 A028351 A028352 * A028354 A028355 A028356
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KEYWORD
| nonn,easy
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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