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Search: id:A120593
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| A120593 |
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G.f. satisfies: 5*A(x) = 4 + x + A(x)^4, starting with [1,1,6]. |
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3
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| 1, 1, 6, 76, 1201, 21252, 402892, 8001412, 164321982, 3461110532, 74358814838, 1623152780808, 35897318940028, 802620009567628, 18112759482614328, 412020809942451504, 9437537418826749369, 217486633306640519124
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n.
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FORMULA
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G.f.: A(x) = 1 + Series_Reversion(1+5*x - (1+x)^4). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(4*n,n)/(3*n+1) * (4+x)^(3*n+1)/5^(4*n+1).
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EXAMPLE
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A(x) = 1 + x + 6*x^2 + 76*x^3 + 1201*x^4 + 21252*x^5 +...
A(x)^4 = 1 + 4*x + 30*x^2 + 380*x^3 + 6005*x^4 + 106260*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+6*x^2+x*O(x^n)); for(i=0, n, A=A-5*A+4+x+A^4); polcoeff(A, n)}
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CROSSREFS
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Cf. A120588 - A120592, A120594 - A120607.
Sequence in context: A053337 A155643 A066797 this_sequence A116874 A030044 A145165
Adjacent sequences: A120590 A120591 A120592 this_sequence A120594 A120595 A120596
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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), Jun 16 2006, Jan 24 2008
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