|
| |
|
|
A012396
|
|
Expansion of e.g.f. exp(arctan(x)*log(x+1)).
|
|
0
|
|
|
|
1, 0, 2, -3, 12, -70, 418, -2604, 20048, -189288, 1883592, -19386840, 226594632, -3022978608, 42088762896, -602721577080, 9458674967808, -163559679584064, 2928052794471360, -53694788632038144
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
Table of n, a(n) for n=0..19.
|
|
|
FORMULA
|
a(n) = n!*sum(k=1..n, 2^(-k)*k!* sum(j=0..n/2-k, ((sum(i=0..2*j, (2^(i+k)*Stirling1(i+k,k)*binomial(2*j+k-1,i+k-1))/(i+k)!))*(-1)^j*Stirling1(n-2*j-k,k))/(n-2*j-k)!)), n>0, a(0)=1. - Vladimir Kruchinin, Jun 01 2011
|
|
|
EXAMPLE
|
exp(arctan(x)*log(x+1)) = 1 + (2/2!)*x^2 - (3/3!)*x^3 + (12/4!)*x^4 - (70/5!)*x^5 + ...
|
|
|
PROG
|
(Maxima)
a(n):=n!*sum(2^(-k)*k!*sum(((sum((2^(i+k)*stirling1(i+k, k)*binomial(2*j+k-1, i+k-1))/(i+k)!, i, 0, 2*j))*(-1)^j*stirling1(n-2*j-k, k))/(n-2*j-k)!, j, 0, n/2-k), k, 1, n); /* Vladimir Kruchinin, Jun 01 2011 */
|
|
|
CROSSREFS
|
Sequence in context: A264726 A099805 A009269 * A013012 A009594 A074179
Adjacent sequences: A012393 A012394 A012395 * A012397 A012398 A012399
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
Patrick Demichel (patrick.demichel(AT)hp.com)
|
|
|
STATUS
|
approved
|
| |
|
|
