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Search: id:A156100
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| A156100 |
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G.f.: A(x) = exp( Sum_{n>=1} (1 + 2^n*x)^n * x^n/n ). |
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+0
5
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| 1, 1, 3, 7, 25, 113, 741, 7181, 101139, 2089283, 61683087, 2600572391, 156100460443, 13231060891179, 1594932996895155, 270715422001769667, 65209448673400087945, 22130613779988110245993
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Compare to g.f. exp( Sum_{m>=1} (1 + x)^m * x^m/m ) of the Fibonacci sequence.
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FORMULA
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G.f.: A(x) = exp(F(x)) where F(x) is the l.g.f. of A156101.
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 25*x^4 + 113*x^5 + 741*x^6 +...
log(A(x)) = (1 + 2*x)*x + (1 + 2^2*x)^2*x^2/2 + (1 + 2^3*x)^3*x^3/3 +...
log(A(x)) = x + 5*x^2/2 + 13*x^3/3 + 65*x^4/4 + 401*x^5/5 + 3521*x^6/6 +...
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PROGRAM
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (1+2^m*x)^m*x^m/m)+x*O(x^n)), n)}
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CROSSREFS
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Cf. A156101 (log), A155810.
Sequence in context: A133206 A054092 A096648 this_sequence A019056 A065163 A057124
Adjacent sequences: A156097 A156098 A156099 this_sequence A156101 A156102 A156103
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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), Feb 04 2009
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