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Search: id:A107591
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| A107591 |
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G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n*(n+1)/2). |
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+0
4
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| 1, 1, 2, 6, 22, 91, 408, 1939, 9635, 49614, 263140, 1431301, 7959568, 45152340, 260847526, 1532825675, 9154581802, 55537885743, 342147577227, 2140251570508, 13594688301758, 87702596534110, 574815620158265, 3829029514213952
(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/G107590(x)) and thus A(x) = G107590(x*A(x)) where G107591(x) is the g.f. of A107590. G.f. A(x) = x/series-reversion(x*G107592(x)) and thus A(x) = G107592(x/A(x)) where G107592(x) is the g.f. of A107592.
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EXAMPLE
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A = 1 + x*A^1 + x^2*A^3 + x^3*A^6 + x^4*A^10 + x^5*A^15 ...
= 1 + (x + x^2 + 2*x^3 + 6*x^4 + 22*x^5 + 91*x^6 +...)
+ (x^2 + 3*x^3 + 9*x^4 + 31*x^5 + 120*x^6 +...)
+ (x^3 + 6*x^4 + 27*x^5 + 116*x^6 +...)
+ (x^4 + 10*x^5 + 65*x^6 +...) +...
= 1 + x + 2*x^2 + 6*x^3 + 22*x^4 + 91*x^5 + 408*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*(j+1)/2)+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
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Cf. A107590, A107592.
Sequence in context: A053617 A089449 A124293 this_sequence A001181 A130579 A107945
Adjacent sequences: A107588 A107589 A107590 this_sequence A107592 A107593 A107594
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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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