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, 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

Links

Table of n, a(n) for n=0..25.

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

Adjacent sequences: A362807 A362808 A362809 * A362811 A362812 A362813

Keyword

nonn

Author

Jodi Spitz, May 04 2023

Extensions

a(7)-a(25) from Vaclav Kotesovec, Nov 18 2023

Status

approved