A184358 a(n) = (n+1)!^2/2^n.

1, 2, 9, 72, 900, 16200, 396900, 12700800, 514382400, 25719120000, 1556006760000, 112032486720000, 9466745127840000, 927741022528320000, 104370865034436000000, 13359470724407808000000, 1930443519676928256000000, 312731850187662377472000000

Offset

0,2

Comments

Self-convolution of A184359.

Links

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

Formula

From Amiram Eldar, Jun 25 2022: (Start)

Sum_{n>=0} 1/a(n) = (BesselI(0, 2*sqrt(2)) - 1)/2.

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

Example

G.f.: A(x) = 1 + 2*x + 9*x^2 + 72*x^3 + 900*x^4 + 16200*x^5 +...
A(x)^(1/2) = 1 + x + 4*x^2 + 32*x^3 + 410*x^4 + 7562*x^5 + 188736*x^6 +...+ A184359(n)*x^n +...

Mathematica

a[n_] := (n + 1)!^2/2^n; Array[a, 20, 0] (* Amiram Eldar, Jun 25 2022 *)

Prog

(PARI) {a(n)=(n+1)!^2/2^n}

Crossrefs

Cf. A184359, A184360, A184361, A006472.

Sequence in context: A133984 A208898 A108995 * A132843 A346648 A336955

Adjacent sequences: A184355 A184356 A184357 * A184359 A184360 A184361

Keyword

nonn

Author

Paul D. Hanna, Jan 16 2011

Status

approved