The On-Line Encyclopedia of Integer Sequences (OEIS)

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A009763 revision #18

A009763

a(n) is (n+1)!*(n+2)! times coefficient of x^n in (log(1-x))^-1.

1, 1, 6, 76, 1620, 51780, 2310000, 136898496, 10393064640, 982930939200, 113269208976000, 15619762139984640, 2539231615282602240, 480507998223110457600, 104704722014993388288000

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OFFSET

0,3

COMMENTS

Related to 'logarithmic numbers'.

LINKS

Table of n, a(n) for n=0..14.

FORMULA

log(2*Pi) = 1 + sum{a(n)*(2n+1)/(((n+1)!)^2*n*(n+1)); n>0} = 1.83787706... = A061444. - Philippe Deléham, Jan 20 2004

Sum_{n>=0} a(n)/((n+1)*(n+1)!*(n+2)!) = Euler constant gamma = 0.5772156649... = A001620. - Philippe Deléham, Feb 26 2004

MATHEMATICA

Table[(n+2)!*Abs[Sum[StirlingS1[n+1, k]/(k+1), {k, 0, n+1}]], {n, 0, 20}] (* Vaclav Kotesovec, Aug 03 2014 *)

PROG

(PARI) a(n)=local(A); if(n<0, 0, n++; A=x/log(1-x+x^2*O(x^n)); n!*(n+1)!*polcoeff(A, n))

CROSSREFS

a(n)=(n+1)!*(n+2)!*A002206/A002207(n).

Sequence in context: A336713 A218303 A132613 * A340886 A305999 A274464

Adjacent sequences: A009760 A009761 A009762 * A009764 A009765 A009766

KEYWORD

nonn

AUTHOR

Philippe Deléham, BP 29 Coconi, 97670 Ouangani, Mayotte.

EXTENSIONS

Better description and more terms from Joe Keane (jgk(AT)jgk.org), Aug 13 2002

STATUS

approved