login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A337151 a(n) = (n!)^2 * Sum_{k=0..n} (-1)^(n-k) * (k+1) / ((n-k)!)^2. 0
1, 1, 5, 53, 977, 27649, 1111429, 60147205, 4213400897, 370767834593, 40025019652901, 5199763957426741, 800136077306754385, 143904538461745813153, 29906871652295426507237, 7111902097369951568209349, 1918658066681198636106335489, 582817397769914314847061436225 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)