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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).
0
0, 0, 1, 6, 30, 173, 1138, 8386, 67951, 596745, 5618916, 56249658, 594648335, 6602123630, 76631632344, 926329705808, 11623455427764, 150970962492188, 2024773236657401, 27980260971851306, 397645587914766071, 5801999753304428181, 86784442260270596447, 1328924296505789704631, 20807559990139289975657, 332753116291423840918784
OFFSET
0,4
COMMENTS
Appears to grow factorially (superexponentially).
Conjecture: limit_{n->oo} log(a(n)) / log(n!) < 1. - Vaclav Kotesovec, Nov 17 2023
EXAMPLE
a(5) = 173 since the local minimum in [0,oo) of the 10th derivative of Gamma(x) is 173.195...
MATHEMATICA
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 *)
CROSSREFS
Cf. A030171.
Sequence in context: A353891 A353880 A175925 * A365273 A110706 A001341
KEYWORD
nonn
AUTHOR
Jodi Spitz, May 04 2023
EXTENSIONS
a(7)-a(25) from Vaclav Kotesovec, Nov 18 2023
STATUS
approved