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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

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Last modified January 31 21:46 EST 2023. Contains 359981 sequences. (Running on oeis4.)