A068939 a(n) = Bell(n^2), where Bell(n) are the Bell numbers, cf. A000110.

1, 1, 15, 21147, 10480142147, 4638590332229999353, 3819714729894818339975525681317, 10726137154573358400342215518590002633917247281

Offset: 0

Author

Karol A. Penson, Mar 08 2002

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..20

Crossrefs

Cf. A000110.

Programs

Magma

[Bell(n^2): n in [0..8]]; // Vincenzo Librandi, Jul 16 2013

Mathematica

Table[BellB[n^2], {n, 0, 8}] (* Vincenzo Librandi, Jul 16 2013 *)

PARI

for(n=0,50,print1(round(sum(i=0,1000,i^(n^2)/(i)!)/exp(1)),","))

Python

from sympy import bell
def A068939(n): return bell(n**2) # Chai Wah Wu, Jun 22 2022

Formula

a(n) = exp(-1)*Sum(k=>0, k^(n^2)/k!). - Benoit Cloitre, May 19 2002

Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*(sum(exp(-ln(x)^2/ (4*ln(k)))/(k!*sqrt(ln(k))), k=2..infinity)/ (2*exp(1)*sqrt(Pi)*x) +Dirac(1-x)/exp(1)), x=0..infinity), n=0, 1, ...