|
|
A300491
|
|
Expansion of e.g.f. log(1 - log(1 - x)/(1 - x)).
|
|
2
|
|
|
0, 1, 2, 4, 9, 28, 140, 936, 6902, 54160, 467784, 4578000, 50434032, 609309504, 7921524624, 110242136928, 1643101763760, 26192405980416, 444523225673472, 7989603260143104, 151483589818925184, 3022296286833907200, 63326051483436129024, 1390571693776506751488
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
log(1 - log(1 - x)/(1 - x)) = x/1! + 2*x^2/2! + 4*x^3/3! + 9*x^4/4! + 28*x^5/5! + 140*x^6/6! + 936*x^7/7! + ...
|
|
MAPLE
|
b:= proc(n) option remember; `if`(n<2, n, n*b(n-1)+(n-1)!) end:
a:= proc(n) option remember; `if`(n=0, 0, b(n)-add(
a(j)*j*binomial(n, j)*b(n-j), j=1..n-1)/n)
end:
|
|
MATHEMATICA
|
nmax = 23; CoefficientList[Series[Log[1 - Log[1 - x]/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = n! HarmonicNumber[n] - Sum[k Binomial[n, k] (n - k)! HarmonicNumber[n - k] a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 23}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|