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A107594
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G.f. satisfies: A(x) = Sum_{n>=0} x^n * A^(n^2-n).
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2
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1, 1, 1, 3, 10, 42, 194, 979, 5274, 30037, 179527, 1120612, 7280750, 49120810, 343547469, 2487670468, 18631824735, 144215785791, 1152745117570, 9508011730755, 80861962283808, 708502494881786, 6390084112199801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| G.f. A(x) = x/series-reversion(x*G107595(x)) and thus A(x) = G107595(x/A(x)) where G107595(x) is the g.f. of A107595. G.f. A(x)^2 = x/series-reversion(x*G107596(x)^2) and thus A(x) = G107596(x/A(x)^2) where G107596(x) is the g.f. of A107596.
Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Apr 25 2010: (Start)
Let A = g.f. A(x), then A satisfies the continued fraction:
A = 1/(1- x/(1- (A^2-1)*x/(1- A^4*x/(1- (A^6-A^2)*x/(1- A^8*x/(1- (A^10-A^4)*x/(1- A^12*x/(1- (A^14-A^6)*x/(1- ...)))))))))
due to an identity of a partial elliptic theta function.
(End)
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EXAMPLE
| A = 1 + x*A^0 + x^2*A^2 + x^3*A^6 + x^4*A^12 + x^5*A^20 ...
= 1 + x + (x^2 + 2*x^3 + 3*x^4 + 8*x^5 + 27*x^6 + 110*x^7 +...)
+ (x^3 + 6*x^4 + 21*x^5 + 68*x^6 + 240*x^7 +...)
+ (x^4 + 12*x^5 + 78*x^6 + 388*x^7 +...) +...
= 1 + x + x^2 + 3*x^3 + 10*x^4 + 42*x^5 + 194*x^6 + 979*x^7 +...
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PROG
| (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-j)+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
| Cf. A107590, A107595, A107596.
Sequence in context: A094558 A074511 A000249 * A094195 A091843 A007552
Adjacent sequences: A107591 A107592 A107593 * A107595 A107596 A107597
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KEYWORD
| eigen,nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 17 2005
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