A268293 - OEIS

%I #7 Feb 08 2016 12:44:57

%S 1,1,4,33,436,8183,204086,6482641,254507098,12071123966,679190315310,

%T 44661150338934,3389246296048276,293668284385781381,

%U 28785799019660366614,3166449702201279923725,388125298319949129243244,52681998287784899631795504,7874555043366017438046929702,1289724117374870730134874529049

%N a(n) = A266489(n)/n, for n>=1.

%C Conjectured to consist entirely of integers.

%H Paul D. Hanna, <a href="/A268293/b268293.txt">Table of n, a(n) for n = 1..300</a>

%F The g.f. of A266489, G(x) = 1 + x*A'(x), satisfies: [x^n] G( x/G(x)^n ) = 0 for n>1.

%e G.f.: A(x) = x + x^2 + 4*x^3 + 33*x^4 + 436*x^5 + 8183*x^6 + 204086*x^7 + 6482641*x^8 + 254507098*x^9 + 12071123966*x^10 +...

%e such that G(x) = 1 + x*A'(x):

%e G(x) = 1 + x + 2*x^2 + 12*x^3 + 132*x^4 + 2180*x^5 + 49098*x^6 + 1428602*x^7 + 51861128*x^8 + 2290563882*x^9 + 120711239660*x^10 +...+ A266489(n)*x^n +...

%e satisfies: [x^n] G( x/G(x)^n ) = 0 for n>1.

%o (PARI) {a(n) = my(A=[1, 1]); for(i=2, n, A=concat(A, 0); A[#A] = -Vec(subst(Ser(A), x, x/Ser(A)^(#A-1)))[#A]); A[n+1]/n}

%o for(n=1, 30, print1(a(n), ", "))

%Y Cf. A266489.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Feb 08 2016