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A118795
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E.g.f.: -1 + exp(( 1 - sqrt(5 - 4*exp(x)) )/2).
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2
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0, 1, 4, 29, 329, 5172, 104335, 2571473, 74894818, 2516911731, 95862252417, 4080739041238, 192000366357981, 9894168501171229, 554208686184384028, 33527021385789228265, 2178482569432714859789, 151314182463701892157460, 11188187745418763137485747
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OFFSET
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0,3
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COMMENTS
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Also equals the unsigned row sums of triangle A118793 (offset without leading zero).
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LINKS
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Table of n, a(n) for n=0..18.
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FORMULA
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a(n) = (n-1)!*Sum_{k=0..n-1} abs( [x^k] (x/log(1-x-x^2))^n/(n-1-k)! ) for n>0.
a(n) = sum(k=1..n, (sum(i=0..n-k, ((i+k-1)!*C(k+2*i-1,i+k-1) *stirling2(n, i+k))))/(k-1)!). [From Vladimir Kruchinin, Nov 22 2011]
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EXAMPLE
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E.g.f.: A(x) = x + 4/2*x^2 + 29/6*x^3 + 329/24*x^4 + 5172/120*x^5 +...
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PROG
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(PARI) {a(n)=local(x=X+X^2*O(X^n)); n!*polcoeff(-1+exp((1-sqrt(5-4*exp(x)))/2), n, X)} (PARI) /* As the unsigned row sums of A118793: */ {a(n)=local(x=X+X^2*O(X^n)); if(n<1, 0, (n-1)!*sum(k=0, n-1, abs(polcoeff(((x/log(1-x-x^2)))^n/(n-1-k)!, k, X))))}
(Maxima) a(n):=sum((sum(((i+k-1)!*binomial(k+2*i-1, i+k-1)*stirling2(n, i+k)), i, 0, n-k))/(k-1)!, k, 1, n); [From Vladimir Kruchinin, Nov 22 2011]
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CROSSREFS
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Cf. A118793, A118794.
Sequence in context: A195194 A215955 A028853 * A099700 A137646 A168602
Adjacent sequences: A118792 A118793 A118794 * A118796 A118797 A118798
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Apr 30 2006
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STATUS
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approved
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