A338633 G.f. A(x) satisfies: 1 = A(x) - x/(A(x) - 2^3*x/(A(x) - 3^3*x/(A(x) - 4^3*x/(A(x) - 5^3*x/(A(x) - 6^3*x/(A(x) - ...)))))), a continued fraction relation.

1, 1, 7, 250, 21867, 3725702, 1096355494, 513875333940, 361121449989171, 362961084011245198, 502496711191618404882, 929337000359116522329132, 2238572532534241145084855934, 6875030222633195280825967544508, 26436454884630260855874989243890732

Offset

0,3

Comments

Compare to the continued fraction relation for the g.f. of A158119 and A338634.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..150

Formula

For n > 0, a(n) is odd iff n is a power of 2 (conjecture).

From Vaclav Kotesovec, Nov 12 2020: (Start)

a(n) ~ sqrt(3/(2*Pi)) * (6*Gamma(2/3)/Gamma(1/3)^2)^(3*n + 3/2) * (n!)^3 / sqrt(n).

a(n) ~ 2^(6*n + 4) * 3^(3*n/2 + 5/4) * Pi^(3*n + 5/2) * n^(3*n + 1) / Gamma(1/3)^(9*(n + 1/2)) / exp(3*n). (End)

Example

G.f.: A(x) = 1 + x + 7*x^2 + 250*x^3 + 21867*x^4 + 3725702*x^5 + 1096355494*x^6 + 513875333940*x^7 + 361121449989171*x^8 + 362961084011245198*x^9 + ...
where
1 = A(x) - x/(A(x) - 2^3*x/(A(x) - 3^3*x/(A(x) - 4^3*x/(A(x) - 5^3*x/(A(x) - 6^3*x/(A(x) - 7^3*x/(A(x) - 8^3*x/(A(x) - 9^3*x/(A(x) - ...))))))))), a continued fraction relation.

Prog

(PARI) {a(n) = my(A=[1], CF=1); for(i=1, n, A=concat(A, 0); for(i=1, #A, CF = Ser(A) - (#A-i+1)^3*x/CF ); A[#A] = -polcoeff(CF, #A-1) ); A[n+1] }
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A000699, A158119, A216966, A338634.

Sequence in context: A229482 A193371 A347843 * A142805 A203474 A366866

Adjacent sequences: A338630 A338631 A338632 * A338634 A338635 A338636

Keyword

nonn

Author

Paul D. Hanna, Nov 04 2020

Status

approved