A354942 a(n) = Sum_{k=0..n} binomial(n,k)^3 * k! * (-3)^(n-k).

1, -2, -13, 60, 1113, 1002, -149049, -1932696, 7188705, 676972566, 10821753819, -32865363468, -5892948042327, -144308265498270, -748826955982593, 74472859430936928, 3199088479682040129, 57854159449349840046, -654712764990637945725, -87482030500940669619156

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

Mathematica

Table[Sum[Binomial[n, k]^3 k! (-3)^(n - k), {k, 0, n}], {n, 0, 19}]
nmax = 19; CoefficientList[Series[BesselI[0, 2 Sqrt[x]] Sum[(-3)^k x^k/k!^3, {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^3

Prog

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

Crossrefs

Cf. A010843, A277386, A343840, A354941.

Sequence in context: A187560 A338818 A290721 * A205532 A294052 A353177

Adjacent sequences: A354939 A354940 A354941 * A354943 A354944 A354945

Keyword

sign

Author

Ilya Gutkovskiy, Jun 12 2022

Status

approved