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%I #21 Sep 22 2024 17:45:46
%S 1,1,2,8,56,728,17472,768768,62270208,9278260992,2542243511808,
%T 1281290729951232,1187756506664792064,2025124843863470469120,
%U 6350791510355843391160320,36631365431732504680212725760,388622155865250142152376807587840
%N Product of tribonacci numbers A000073(2) * ... * A000073(n).
%H Chai Wah Wu, <a href="/A254231/b254231.txt">Table of n, a(n) for n = 2..89</a>
%F 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... .
%t Table[Product[SeriesCoefficient[x^2/(1-x-x^2-x^3),{x,0,k}],{k,2,n}], {n,2,20}]
%o (Python)
%o A254231_list, a, b, c, d = [1], 0, 0, 1, 1
%o for _ in range(15):
%o a, b, c = b, c, a+b+c
%o d *= c
%o A254231_list.append(d) # _Chai Wah Wu_, Jan 27 2015
%Y Cf. A000073, A003266, A058265, A126772, A135407, A254232.
%K nonn
%O 2,3
%A _Vaclav Kotesovec_, Jan 27 2015