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A049034 Scaled sums of odd reciprocals. 6
1, 8, 184, 8448, 648576, 74972160, 12174658560, 2643856588800, 740051782041600, 259500083163955200, 111422936937037824000, 57504006817918746624000, 35122852492484487413760000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) mod n^2 = 2*n if n is an odd prime, otherwise 0. - Gary Detlefs, Apr 16 2012

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..224

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)!.

EXAMPLE

(arctanh x)^2 = x^2 + 2/3*x^4 + 23/45*x^6 + 44/105*x^8 + ...

MATHEMATICA

Module[{nn=25, c}, c=Range[1, nn, 2]; Times@@@Thread[{Accumulate[1/c], c!}]](* Harvey P. Dale, Nov 20 2013 *)

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 */

CROSSREFS

Cf. A000254, A004041, A046674. a(n)=A081358(2n+1).

Sequence in context: A024286 A231795 A240319 * A092546 A227584 A197894

Adjacent sequences:  A049031 A049032 A049033 * A049035 A049036 A049037

KEYWORD

nonn

AUTHOR

Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.