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A049034
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Scaled sums of odd reciprocals.
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5
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1, 8, 184, 8448, 648576, 74972160, 12174658560, 2643856588800, 740051782041600, 259500083163955200, 111422936937037824000, 57504006817918746624000, 35122852492484487413760000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = (2*n+1)! * sum[ k=0..n ] 1/(2*k+1).
E.g.f. (arctanh x)^2/2 = sum_n a(n)x^(2n+2)/(2n+2)! or (arctanh x)/(1-x^2) = sum_n a(n)x^(2n+1)/(2n+1)!.
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EXAMPLE
| (arctanh x)^2 = x^2 + 2/3*x^4 + 23/45*x^6 + 44/105*x^8 + ...
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PROG
| (PARI) {a(n)=if(n<0, 0, n=2*n+1; n!*sum(k=1, n, (k%2)/k))} /* Michael Somos Sep 19 2006 */
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CROSSREFS
| Cf. A000254, A004041, A046674. a(n)=A081358(2n+1).
Sequence in context: A203359 A180607 A024286 * A092546 A197894 A198011
Adjacent sequences: A049031 A049032 A049033 * A049035 A049036 A049037
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KEYWORD
| nonn
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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