A134358 Coefficient of y^(n-3) in expansion of (y+n!)^n.

216, 55296, 17280000, 7464960000, 4480842240000, 3670705963008000, 4013916970549248000, 5734167100784640000000, 10494242565323489280000000, 24178734870505319301120000000, 69056884663650242455928832000000, 241171752839889792198814728192000000, 1017443332293285060838749634560000000000

Offset

3,1

Links

Table of n, a(n) for n=3..15.

Formula

a(n) = (n!)^m/m! * Product_{k=0..m-1} (n-k), here with m=3. - Georg Fischer, Feb 11 2026

Mathematica

a = {}; Do[k = CoefficientList[Expand[(y + n!)^n], y]; AppendTo[a, k[[Length[k] - 3]]], {n, 3, 50}]; a

Crossrefs

Cf. A001563 (m=1), A131092 (m=2), A134359 (m=4).

Sequence in context: A206697 A299994 A124009 * A167127 A269821 A268364

Adjacent sequences: A134355 A134356 A134357 * A134359 A134360 A134361

Keyword

nonn,easy

Author

Artur Jasinski, Oct 22 2007

Extensions

a(14)-a(15) from Georg Fischer, Feb 11 2026

Status

approved