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A274569 G.f. satisfies: A( x*A(x) ) = x^2 + x^3. 1

%I

%S 1,1,-1,-2,2,9,1,-29,-24,88,153,-234,-796,327,3509,1301,-13924,-16511,

%T 47366,109639,-121886,-583921,79027,2691465,1808431,-10775705,

%U -16965876,35686874,107103382,-77820607,-560120299,-95094380,2536045800,2521002564,-9832805334,-19928899203,29983217002,118838292930,-44109504096,-600237397739,-285632368107,2622720919077,3530864633371,-9611558966277,-24857829812388,25472208656701,140445352832736,-5891793579597,-680872708032455,-537359624615144,2838471301330439,4957200244969051,-9600812793387365

%N G.f. satisfies: A( x*A(x) ) = x^2 + x^3.

%H Paul D. Hanna, <a href="/A274569/b274569.txt">Table of n, a(n) for n = 1..500</a>

%e G.f.: A(x) = x + x^2 - x^3 - 2*x^4 + 2*x^5 + 9*x^6 + x^7 - 29*x^8 - 24*x^9 + 88*x^10 + 153*x^11 - 234*x^12 - 796*x^13 + 327*x^14 + 3509*x^15 + 1301*x^16 +...

%e such that A( x*A(x) ) = x^2 + x^3.

%p N:= 50: # to get a(1) to a(N)

%p a[1]:= 1:

%p eq:= eval(A(x*A(x)) - x^2 - x^3, A = unapply(add(a[i]*x^i,i=1..N),x)):

%p S:= map(normal,series(eq,x,N+2)):

%p for n from 2 to N+1 do

%p a[n]:= solve(coeff(S,x,n+1))

%p od:

%p seq(a[i],i=1..50); # _Robert Israel_, Jul 26 2016

%o (PARI) {a(n) = my(A=[1,1],F); for(i=1,n, A=concat(A,0); F=x*Ser(A); F = subst(F,x,x*F); A[#A] = -Vec(F)[#A]); A[n]}

%o for(n=1,60, print1(a(n),", "))

%K sign

%O 1,4

%A _Paul D. Hanna_, Jul 18 2016

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Last modified October 14 07:19 EDT 2019. Contains 327995 sequences. (Running on oeis4.)