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A012396
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E.g.f. exp(arctan(x)*log(x+1)).
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0
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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; internal format)
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OFFSET
| 0,3
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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. [From Vladimir Kruchinin, Jun 01 2011]
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EXAMPLE
| exp(arctan(x)*log(x+1))=1+2/2!*x^2-3/3!*x^3+12/4!*x^4-70/5!*x^5...
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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); [From Vladimir Kruchinin, Jun 01 2011]
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CROSSREFS
| Sequence in context: A012911 A099805 A009269 * A013012 A009594 A074179
Adjacent sequences: A012393 A012394 A012395 * A012397 A012398 A012399
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KEYWORD
| sign
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AUTHOR
| Patrick Demichel (dml(AT)hpfrcu03.france.hp.com)
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