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Search: id:A107945
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| A107945 |
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G.f. A(x) satisfies: A(x) = x*f(A,A^2/x) where f(,) is Ramanujan's theta function; i.e., A(x) = x*Sum_{n=-oo,+oo} A^(n*(n+1)/2)*(A^2/x)^(n*(n-1)/2)). |
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+0
2
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| 1, 2, 6, 22, 92, 424, 2100, 10952, 59220, 328454, 1855548, 10630282, 61585456, 360139296, 2123022032, 12603671392, 75291625002, 452279294266, 2730374221784, 16556643025496, 100801159909630, 615936184506514
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A variant of sequence A107902 by Michael Somos.
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FORMULA
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G.f. satisfies: A(x) = x/Sum_{n=-oo, +oo} x^(-n*(n-1)/2)*A(x)^(n*(3*n-1)/2)). G.f.: A(x) = series_reversion(x^2/G107902(x)) where G107902(x) is g.f. of A107902.
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EXAMPLE
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A(x) = x + 2*x^2 + 6*x^3 + 22*x^4 + 92*x^5 + 424*x^6 + 2100*x^7 +...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, A=x+O(x^2); for(k=2, n, A=x*sum(i=-sqrtint(n-1), sqrtint(n+2), x^(-(i^2-i)/2)*A^((3*i^2-i)/2))); polcoeff(A, n))}
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CROSSREFS
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Cf. A107902, A107944.
Adjacent sequences: A107942 A107943 A107944 this_sequence A107946 A107947 A107948
Sequence in context: A107591 A001181 A130579 this_sequence A014330 A124294 A124295
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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), May 28 2005
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