|
|
A087301
|
|
a(n) = n!*Sum_{i=1..n-1} (-1)^(i+1)/i.
|
|
1
|
|
|
2, 3, 20, 70, 564, 3108, 30624, 230256, 2705760, 25771680, 352805760, 4067556480, 63651813120, 861371884800, 15176802816000, 235775183616000, 4620563523072000, 81032645804544000, 1748700390205440000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,1
|
|
COMMENTS
|
Stirling transform of A052882(n)=[0,2,9,52,375,...] is a(n+1)=[0,2,3,20,...]. - Michael Somos, Mar 04 2004
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: x*log(1+x)/(1-x). a(n) = 1/2*(-1)^n*n!*(2*(-1)^n*log(2)+Psi(1/2+1/2*n)-Psi(1/2*n)).
|
|
MATHEMATICA
|
Rest[Table[n!Sum[(-1)^(i+1)/i, {i, n-1}], {n, 20}]] (* Harvey P. Dale, Oct 24 2011 *)
|
|
PROG
|
(PARI) a(n)=if(n<0, 0, n!*polcoeff(log(1+x+x*O(x^n))*x/(1-x), n))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|