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Search: id:A158873
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| A158873 |
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L.g.f.: Sum_{n>=1} a(n)*x^n/n = Sum_{n>=1} (1 + a(n)*x)^n * x^n/n. |
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+0
3
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| 1, 3, 10, 59, 796, 38106, 10575020, 37219912979, 4683360721197196, 107669805691203995115748, 4936018245619051863546606625582972, 12131323997867394119748184355028213021384527189930
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = 1 + n*Sum_{k=1..[n/2]} C(n-k,k)*a(n-k)^k/(n-k) for n>1 with a(1)=1.
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EXAMPLE
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L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 59*x^4/4 + 796*x^5/5 +...
L(x) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+10*x)^3*x^3/3 + (1+59*x)^4*x^4/4 +...
exp(L(x)) = g.f. of A158872 is an integer series:
exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 20*x^4 + 182*x^5 + 6552*x^6 +...
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PROGRAM
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(PARI) {a(n)=1+n*sum(k=1, n\2, binomial(n-k, k)*a(n-k)^k/(n-k))}
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CROSSREFS
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Cf. A158872 (exp).
Sequence in context: A111270 A112101 A159321 this_sequence A103591 A018932 A111562
Adjacent sequences: A158870 A158871 A158872 this_sequence A158874 A158875 A158876
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2009
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