cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A362810 Define G(n, k) to be the n-th derivative of Gamma(x) at k. a(n)=floor(min(G(2n, x))), where min(f) is the local minimum of f in [0,oo).

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%I A362810 #19 Nov 18 2023 03:18:36
%S A362810 0,0,1,6,30,173,1138,8386,67951,596745,5618916,56249658,594648335,
%T A362810 6602123630,76631632344,926329705808,11623455427764,150970962492188,
%U A362810 2024773236657401,27980260971851306,397645587914766071,5801999753304428181,86784442260270596447,1328924296505789704631,20807559990139289975657,332753116291423840918784
%N A362810 Define G(n, k) to be the n-th derivative of Gamma(x) at k. a(n)=floor(min(G(2n, x))), where min(f) is the local minimum of f in [0,oo).
%C A362810 Appears to grow factorially (superexponentially).
%C A362810 Conjecture: limit_{n->oo} log(a(n)) / log(n!) < 1. - _Vaclav Kotesovec_, Nov 17 2023
%e A362810 a(5) = 173 since the local minimum in [0,oo) of the 10th derivative of Gamma(x) is 173.195...
%t A362810 Join[{0}, Floor[Table[d = Simplify[D[Gamma[x], {x, 2 n}]]; d /. FindRoot[D[d, x] == 0, {x, n/2}, WorkingPrecision -> 50], {n, 1, 10}]]] (* _Vaclav Kotesovec_, Nov 17 2023 *)
%Y A362810 Cf. A030171.
%K A362810 nonn
%O A362810 0,4
%A A362810 _Jodi Spitz_, May 04 2023
%E A362810 a(7)-a(25) from _Vaclav Kotesovec_, Nov 18 2023