A254231 Product of tribonacci numbers A000073(2) * ... * A000073(n).

1, 1, 2, 8, 56, 728, 17472, 768768, 62270208, 9278260992, 2542243511808, 1281290729951232, 1187756506664792064, 2025124843863470469120, 6350791510355843391160320, 36631365431732504680212725760, 388622155865250142152376807587840

Offset: 2

Author

Vaclav Kotesovec, Jan 27 2015

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..89

Crossrefs

Cf. A000073, A003266, A058265, A126772, A135407, A254232.

Programs

Mathematica

Table[Product[SeriesCoefficient[x^2/(1-x-x^2-x^3),{x,0,k}],{k,2,n}], {n,2,20}]

Python

A254231_list, a, b, c, d = [1], 0, 0, 1, 1
for _ in range(15):
    a, b, c = b, c, a+b+c
    d *= c
    A254231_list.append(d) # Chai Wah Wu, Jan 27 2015

Formula

a(n) ~ c * d^(n/2) * r^(n^2/2), where r = A058265 = 1.839286755214161132551852564653286600424178746097592246778758639404203222... is the root of the equation r^3 - r^2 - r - 1 = 0, d = 0.061463687669952618841340986526101395138659648898940720192319213600612851... is the root of the equation -1 + 36*d - 440*d^2 + 1936*d^3 = 0, c = 4.156714772910304733054135311449211887936035199917470476143821433373978333... .