A340789 a(n) = (n!)^2 * Sum_{k=1..n} (-1)^(k+1) / (k!)^2.

0, 1, 3, 28, 447, 11176, 402335, 19714416, 1261722623, 102199532464, 10219953246399, 1236614342814280, 178072465365256319, 30094246646728317912, 5898472342758750310751, 1327156277120718819918976, 339752006942904017899257855, 98188330006499261172885520096

Offset: 0

Author

Ilya Gutkovskiy, Jan 23 2021

Keywords

• nonn

Crossrefs

Cf. A002467, A006040, A066998, A073701.

Programs

Mathematica

Table[n!^2 Sum[(-1)^(k + 1)/k!^2, {k, 1, n}], {n, 0, 17}]
nmax = 17; CoefficientList[Series[(1 - BesselJ[0, 2 Sqrt[x]])/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!^2

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = (1 - BesselJ(0,2*sqrt(x))) / (1 - x).

a(0) = 0; a(n) = n^2 * a(n-1) - (-1)^n.