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Search: id:A144005
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| A144005 |
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E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral A(-x) dx ). |
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2
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| 1, 1, 1, 2, 7, 33, 201, 1479, 12842, 127952, 1440989, 18070767, 249766088, 3769280801, 61654447712, 1085974748430, 20485430748783, 411839042136379, 8786499316562396, 198174104269740313, 4708919322491690592
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Is this sequence equal to A014623 (related to Levine's sequence A011784)?
Compare the definition of e.g.f. A(x) to the trivial statement:
if F(x) = 1 + Series_Reversion( Integral F(-x)^2 dx ) then F(x) = 1/(1-x).
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EXAMPLE
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E.g.f: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 7*x^4/4! + 33*x^5/5! +...
Let I(x) = Series_Reversion(A(x) - 1) = Integral A(-x) dx then
I(x) = x - x^2/2! + x^3/3! - 2*x^4/4! + 7*x^5/5! - 33*x^6/6! +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+serreverse(intformal(subst(A, x, -x)^1))); n!*polcoeff(A, n)}
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CROSSREFS
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Cf. A014623; A144002.
Sequence in context: A059099 A020103 A014623 this_sequence A143889 A023053 A058915
Adjacent sequences: A144002 A144003 A144004 this_sequence A144006 A144007 A144008
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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), Sep 07 2008
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