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Search: id:A157133
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| A157133 |
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G.f. satisfies: A(x) = Sum_{n>=0} x^(n(n+1)/2) * A(x)^n. |
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4
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| 1, 1, 1, 2, 4, 7, 14, 30, 62, 129, 278, 604, 1313, 2883, 6386, 14203, 31733, 71272, 160725, 363670, 825653, 1880351, 4293985, 9830499, 22558939, 51880565, 119552907, 276012657, 638348123, 1478749229, 3430799333, 7971134523
(list; graph; listen)
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OFFSET
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0,4
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 7*x^5 + 14*x^6 + 30*x^7 +...
A(x)^2 = 1 + 2*x + 3*x^2 + 6*x^3 + 13*x^4 + 26*x^5 + 54*x^6 +...
A(x)^3 = 1 + 3*x + 6*x^2 + 13*x^3 + 30*x^4 + 66*x^5 + 145*x^6 +...
A(x)^4 = 1 + 4*x + 10*x^2 + 24*x^3 + 59*x^4 + 140*x^5 + 326*x^6 +...
where
A(x) = 1 + x*A(x) + x^3*A(x)^2 + x^6*A(x)^3 + x^10*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(2*n+1), x^(m*(m+1)/2)*A^m))); polcoeff(A, n)}
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CROSSREFS
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Cf. A157134, A157135, A157136.
Sequence in context: A119268 A002989 A000671 this_sequence A120262 A013326 A074663
Adjacent sequences: A157130 A157131 A157132 this_sequence A157134 A157135 A157136
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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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