A268293 a(n) = A266489(n)/n, for n>=1.

1, 1, 4, 33, 436, 8183, 204086, 6482641, 254507098, 12071123966, 679190315310, 44661150338934, 3389246296048276, 293668284385781381, 28785799019660366614, 3166449702201279923725, 388125298319949129243244, 52681998287784899631795504, 7874555043366017438046929702, 1289724117374870730134874529049

Offset

1,3

Comments

Conjectured to consist entirely of integers.

Links

Paul D. Hanna, Table of n, a(n) for n = 1..300

Formula

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

Example

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 +...
such that G(x) = 1 + x*A'(x):
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 +...
satisfies: [x^n] G( x/G(x)^n ) = 0 for n>1.

Prog

(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}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A266489.

Sequence in context: A192548 A119821 A102321 * A193421 A179421 A356834

Adjacent sequences: A268290 A268291 A268292 * A268294 A268295 A268296

Keyword

nonn

Author

Paul D. Hanna, Feb 08 2016

Status

approved