|
|
A009763
|
|
a(n) is (n+1)!*(n+2)! times coefficient of x^n in (log(1-x))^-1.
|
|
2
|
|
|
1, 1, 6, 76, 1620, 51780, 2310000, 136898496, 10393064640, 982930939200, 113269208976000, 15619762139984640, 2539231615282602240, 480507998223110457600, 104704722014993388288000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Related to 'logarithmic numbers'.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Better description and more terms from Joe Keane (jgk(AT)jgk.org), Aug 13 2002
|
|
STATUS
|
approved
|
|
|
|