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Search: id:A157134
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| A157134 |
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G.f. satisfies: A(x) = Sum_{n>=0} x^(n^2) * A(x)^n. |
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+0
4
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| 1, 1, 1, 1, 2, 4, 7, 11, 18, 33, 63, 117, 211, 383, 713, 1348, 2547, 4793, 9039, 17165, 32785, 62761, 120243, 230768, 444119, 857015, 1656931, 3207990, 6219994, 12079544, 23496417, 45767352, 8, 9256038, 174269488, 340646238, 666604642
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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G.f. satisfies: A(x) = B(x/A(x)) where B(x) = A(x*B(x)) = g.f. of A157135,
where A157135(n) = [x^n] A(x)^(n+1)/(n+1) for n>=0,
and a(n) = [x^n] -1/B(x)^(n-1)/(n-1) for n>1.
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 4*x^5 + 7*x^6 + 11*x^7 +...
A(x)^2 = 1 + 2*x + 3*x^2 + 4*x^3 + 7*x^4 + 14*x^5 + 27*x^6 +...
A(x)^3 = 1 + 3*x + 6*x^2 + 10*x^3 + 18*x^4 + 36*x^5 + 73*x^6 +...
A(x)^4 = 1 + 4*x + 10*x^2 + 20*x^3 + 39*x^4 + 80*x^5 + 168*x^6 +...
where
A(x) = 1 + x*A(x) + x^4*A(x)^2 + x^9*A(x)^3 + x^16*A(x)^4 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, (A=sum(m=0, sqrtint(n), x^(m^2)*A^m))); polcoeff(A, n)}
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CROSSREFS
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Cf. A157135, A157133, A157136.
Sequence in context: A018063 A000570 A023426 this_sequence A127926 A078513 A024622
Adjacent sequences: A157131 A157132 A157133 this_sequence A157135 A157136 A157137
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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 24 2009
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