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Search: id:A107595
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| A107595 |
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G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2). |
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+0
3
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| 1, 1, 2, 7, 31, 158, 884, 5292, 33385, 219797, 1500449, 10573815, 76688602, 571232869, 4363912280, 34161879247, 273906591562, 2248935278231, 18909284838057, 162842178607893, 1436660527685476, 12988076148036405
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f. A(x) = (1/x)*series-reversion(x/G107594(x)) and thus A(x) = G107594(x*A(x)) where G107594(x) is the g.f. of A107594. G.f. A(x) = x/series-reversion(x*G107596(x)) and thus A(x) = G107596(x/A(x)) where G107596(x) is the g.f. of A107596.
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EXAMPLE
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A = 1 + x*A^1 + x^2*A^4 + x^3*A^9 + x^4*A^16 + x^5*A^25 ...
= 1 + (x + x^2 + 2*x^3 + 7*x^4 + 31*x^5 + 158*x^6 +...)
+ (x^2 + 4*x^3 + 14*x^4 + 56*x^5 + 257*x^6 +...)
+ (x^3 + 9*x^4 + 54*x^5 + 291*x^6 + 1557*x^7 +..)
+ (x^4 + 16*x^5 + 152*x^6 + 1152*x^7 +...) +...
= 1 + x + 2*x^2 + 7*x^3 + 31*x^4 + 158*x^5 + 884*x^6 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^(j^2)+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
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Cf. A107590, A107594, A107596.
Sequence in context: A030913 A030945 A088554 this_sequence A030882 A030966 A009132
Adjacent sequences: A107592 A107593 A107594 this_sequence A107596 A107597 A107598
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KEYWORD
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eigen,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 17 2005
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