A354944 a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-n)^(n-k).

1, 0, -10, 60, 1560, -39880, -491760, 45672060, -155935360, -77656158000, 2116774828800, 166585352850620, -11925674437248000, -330617542587341880, 69148933431781898240, -543549949643024194500, -434534462104188331130880, 21521903478880966780355360

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = n!^3 * [x^n] BesselI(0,2*sqrt(x)) * Sum_{k>=0} (-n)^k * x^k / k!^3.

Mathematica

Unprotect[Power]; 0^0 = 1; Table[Sum[Binomial[n, k]^3 k! (-n)^(n - k), {k, 0, n}], {n, 0, 17}]
Unprotect[Power]; 0^0 = 1; Table[n!^3 SeriesCoefficient[BesselI[0, 2 Sqrt[x]] Sum[(-n)^k x^k/k!^3, {k, 0, n}], {x, 0, n}], {n, 0, 17}]

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)^3 * k! * (-n)^(n-k)); \\ Michel Marcus, Jun 12 2022

Crossrefs

Cf. A134095, A277423, A336180, A343840, A354941, A354942, A354943.

Sequence in context: A052664 A090373 A218427 * A041184 A089034 A261938

Adjacent sequences: A354941 A354942 A354943 * A354945 A354946 A354947

Keyword

sign

Author

Ilya Gutkovskiy, Jun 12 2022

Status

approved