A337151 a(n) = (n!)^2 * Sum_{k=0..n} (-1)^(n-k) * (k+1) / ((n-k)!)^2.

1, 1, 5, 53, 977, 27649, 1111429, 60147205, 4213400897, 370767834593, 40025019652901, 5199763957426741, 800136077306754385, 143904538461745813153, 29906871652295426507237, 7111902097369951568209349, 1918658066681198636106335489, 582817397769914314847061436225

Offset

0,3

Links

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

Formula

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

Maple

a:= n-> n!^2 * add((-1)^k*(n-k+1)/k!^2, k=0..n):
seq(a(n), n=0..20);  # Alois P. Heinz, Jan 27 2021

Mathematica

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

Crossrefs

Cf. A000255, A073701, A336809.

Sequence in context: A196659 A128943 A180351 * A171192 A330435 A113068

Adjacent sequences: A337148 A337149 A337150 * A337152 A337153 A337154

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 27 2021

Status

approved