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Search: id:A120596
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| A120596 |
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G.f. satisfies: 6*A(x) = 5 + x + A(x)^5, starting with [1,1,10]. |
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3
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| 1, 1, 10, 210, 5505, 161601, 5082420, 167451780, 5705082795, 199354509755, 7105393162010, 257312347583330, 9440808323869455, 350189693739455535, 13110655796699158800, 494772468434359266960, 18801468275832345890970
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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+6*x - (1+x)^5). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(5*n,n)/(4*n+1) * (5+x)^(4*n+1)/6^(5*n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 24 2008
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EXAMPLE
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A(x) = 1 + x + 10*x^2 + 210*x^3 + 5505*x^4 + 161601*x^5 +...
A(x)^5 = 1 + 5*x + 60*x^2 + 1260*x^3 + 33030*x^4 + 969606*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+10*x^2+x*O(x^n)); for(i=0, n, A=A-6*A+5+x+A^5); polcoeff(A, n)}
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CROSSREFS
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Cf. A120588 - A120595, A120597 - A120607.
Sequence in context: A052246 A001450 A076803 this_sequence A057408 A002967 A007698
Adjacent sequences: A120593 A120594 A120595 this_sequence A120597 A120598 A120599
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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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