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A135906 G.f.: A(x) = 1 + x*[A_2(x)]^2, where A_2(x) = 2 + x*[A_3(x)]^2, A_3(x) = 3 + x*[A_4(x)]^2, ..., A_n(x) = n + x*[A_{n+1}(x)]^2, ... 0
1, 4, 36, 465, 7552, 145144, 3191724, 78633536, 2139797572, 63661720934, 2054750445056, 71506836054768, 2669607994059332, 106461335627737280, 4518074113214973200, 203369587888867105097, 9680278850211643305728 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
EXAMPLE
G.f. A(x) = 1 + x*(2 + x*(3 + x*(4 + x*(5 +...)^2 )^2 )^2 )^2.
Initial nested functions, A_n(x) = n + x*[A_{n+1}(x)]^2, begin:
A(x) = 1 + 4x + 36x^2 + 465x^3 + 7552x^4 + 145144x^5 +...
A_2(x) = 2 + 9x + 96x^2 + 1456x^3 + 27430x^4 + 604608x^5 +...
A_3(x) = 3 + 16x + 200x^2 + 3505x^3 + 75408x^4 + 1879328x^5 +...
A_4(x) = 4 + 25x + 360x^2 + 7176x^3 + 173866x^4 + 4839640x^5 +...
A_5(x) = 5 + 36x + 588x^2 + 13153x^3 + 354688x^4 + 10913640x^5 +...
A_6(x) = 6 + 49x + 896x^2 + 22240x^3 + 660942x^4 + 22285664x^5 +...;
In general, A_n(x) = n + (n+1)^2*x + 2(n+1)(n+2)^2*x^2 + [4(n+1)(n+2)(n+3)^2+(n+2)^4]x^3 + [8(n+1)(n+2)(n+3)(n+4)^2+2(n+1)(n+3)^4+4(n+2)^3(n+3)^2]x^4 +...
PROG
(PARI) {a(n)=local(A=n+1+x*(n+2)^2); if(n==0, 1, for(i=0, n-1, A=(n-i+x*(A+x*O(x^n))^2)); polcoeff(A, n))}
CROSSREFS
Sequence in context: A307903 A213596 A009533 * A197446 A291313 A002690
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 05 2007
STATUS
approved

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Last modified May 27 23:25 EDT 2023. Contains 362992 sequences. (Running on oeis4.)