A211825 G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x) )^4.
1, 1, 8, 120, 2528, 66704, 2080128, 74115840, 2952926720, 129637843968, 6205231472640, 321275171444736, 17880710254829568, 1064356462925701120, 67476012302577762304, 4539384115900126199808, 323034928746773883518976, 24248087962137553507450880
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 8*x^2 + 120*x^3 + 2528*x^4 + 66704*x^5 + 2080128*x^6 +... Related expansions: d/dx x*A(x) = 1 + 2*x + 24*x^2 + 480*x^3 + 12640*x^4 + 400224*x^5 +... A'(x) = 1 + 16*x + 360*x^2 + 10112*x^3 + 333520*x^4 + 12480768*x^5 +...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..260
Programs
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PARI
{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x*deriv(x*A)^4);polcoeff(A,n)} for(n=0,25,print1(a(n),", "))
Formula
G.f. satisfies: A(x) = 1 + x*(A(x) + x*A'(x))^4.
a(n) ~ c * 4^n * n! * n^(3/2), where c = 0.06185263969861377609335... - Vaclav Kotesovec, Aug 24 2017