A120600 G.f. satisfies: 7*A(x) = 6 + x + A(x)^6, starting with [1,1,15].
1, 1, 15, 470, 18390, 805806, 37828981, 1860433080, 94614523740, 4935081398830, 262560448214031, 14193030016877406, 777315341935068820, 43039297954660894560, 2405249540028525971070, 135492504636185052358656
Offset: 0
Keywords
Examples
A(x) = 1 + x + 15*x^2 + 470*x^3 + 18390*x^4 + 805806*x^5 +... A(x)^6 = 1 + 6*x + 105*x^2 + 3290*x^3 + 128730*x^4 + 5640642*x^5 +...
Programs
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Mathematica
CoefficientList[1 + InverseSeries[Series[1+7*x - (1+x)^6, {x, 0, 20}], x], x] (* Vaclav Kotesovec, Nov 28 2017 *) -
PARI
{a(n)=local(A=1+x+15*x^2+x*O(x^n));for(i=0,n,A=A-7*A+6+x+A^6);polcoeff(A,n)}
Formula
G.f.: A(x) = 1 + Series_Reversion(1+7*x - (1+x)^6). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(6*n,n)/(5*n+1) * (6+x)^(5*n+1)/7^(6*n+1). - Paul D. Hanna, Jan 24 2008
a(n) ~ (-6 + 5*(7/6)^(6/5))^(1/2 - n) / (2^(3/5) * 3^(1/10) * 7^(2/5) * n^(3/2) * sqrt(5*Pi)). - Vaclav Kotesovec, Nov 28 2017
Comments