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Search: id:A120604
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| A120604 |
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G.f. satisfies: 24*A(x) = 23 + 64*x + A(x)^8, starting with [1,4,28]. |
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+0
3
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| 1, 4, 28, 616, 15820, 453208, 13894552, 445970128, 14796844588, 503423385080, 17467725995720, 615756709476272, 21990183407958584, 793912445913712496, 28928560840589374640, 1062498482335560005024, 39293868860176487815916
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OFFSET
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0,2
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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+24*x - (1+x)^8)/64). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(8*n,n)/(7*n+1) * (23+64*x)^(7*n+1)/24^(8*n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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EXAMPLE
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A(x) = 1 + 4*x + 28*x^2 + 616*x^3 + 15820*x^4 + 453208*x^5 +...
A(x)^8 = 1 + 32*x + 672*x^2 + 14784*x^3 + 379680*x^4 + 10876992*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+4*x+28*x^2+x*O(x^n)); for(i=0, n, A=A+(-24*A+23+64*x+A^8)/16); polcoeff(A, n)}
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CROSSREFS
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Cf. A120588 - A120603, A120605 - A120607.
Sequence in context: A134048 A091969 A101346 this_sequence A081792 A084594 A000838
Adjacent sequences: A120601 A120602 A120603 this_sequence A120605 A120606 A120607
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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
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