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Search: id:A107596
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| A107596 |
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G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2+n). |
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+0
3
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| 1, 1, 3, 14, 80, 514, 3567, 26153, 199900, 1579107, 12816020, 106421359, 901430144, 7771535382, 68085001080, 605420138920, 5459655601753, 49904765136264, 462228258349278, 4337787743946224, 41249375376404380, 397572319756235577
(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)^2 = (1/x)*series-reversion(x/G107594(x)^2) and thus A(x) = G107594(x*A(x)^2) where G107594(x) is the g.f. of A107594. G.f. A(x) = (1/x)*series-reversion(x/G107595(x)) and thus A(x) = G107595(x*A(x)) where G107595(x) is the g.f. of A107595.
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EXAMPLE
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A = 1 + x*A^2 + x^2*A^6 + x^3*A^12 + x^4*A^20 + x^5*A^30 ...
= 1 + (x + 2*x^2 + 7*x^3 + 34*x^4 + 197*x^5 + 1272*x^6 +...)
+ (x^2 + 6*x^3 + 33*x^4 + 194*x^5 + 1230*x^6 +...)
+ (x^3 + 12*x^4 + 102*x^5 + 784*x^6 +...)
+ (x^4 + 20*x^5 + 250*x^6 +...) +...
= 1 + x + 3*x^2 + 14*x^3 + 80*x^4 + 514*x^5 + 3567*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+j)+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
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Cf. A107592, A107594, A107595.
Sequence in context: A020089 A027614 A121873 this_sequence A000264 A009053 A077054
Adjacent sequences: A107593 A107594 A107595 this_sequence A107597 A107598 A107599
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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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