A294352 Product of first n terms of the binomial transform of the factorial.

1, 2, 10, 160, 10400, 3390400, 6635012800, 90899675360000, 9962695319131360000, 9827302289744364817600000, 96937502343569678741652977600000, 10518214548789290471667075399621491200000, 13695360582395151673134516587047571322777664000000

Offset

0,2

Links

Michael De Vlieger, Table of n, a(n) for n = 0..43

M. Bahrami-Taghanaki, A. R. Moghaddamfar, Nima Salehy, and Navid Salehy, Some Identities Involving Stirling Numbers Arising from Matrix Decompositions, J. Int. Seq. (2024) Vol. 24, No. 5, Art. No. 24.5.3. See p. 9.

Formula

a(n) ~ c * exp(n+1) * BarnesG(n+2).

a(n) ~ c * n^(n^2/2 + n + 5/12) * (2*Pi)^(n/2 + 1/2) / (A * exp(3*n^2/4 - 13/12))

where c = 0.24314714161123874545254157058990661627416712475691705561000082745...

and A is the Glaisher-Kinkelin constant A074962.

Mathematica

Table[Product[Sum[Binomial[m, k]*k!, {k, 0, m}], {m, 0, n}], {n, 0, 12}]

Crossrefs

Cf. A000522, A047656, A086619, A294353.

Sequence in context: A134088 A076659 A197313 * A007131 A126449 A328812

Adjacent sequences: A294349 A294350 A294351 * A294353 A294354 A294355

Keyword

nonn,changed

Author

Vaclav Kotesovec, Oct 29 2017

Status

approved