OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..430
FORMULA
a(n) = a(n-1) + 2*(n-1)*n*a(n-2) + (n-2)*(n-1)*(2*n+1)*a(n-3) - (n-10)*(n-3)*(n-2)*(n-1)*a(n-4) - 4*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6) + 2*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-7) + 2*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-8) - (n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-10). - Vaclav Kotesovec, Dec 02 2021
a(n) ~ exp(-101/144 + 29*n^(1/4)/(36*2^(3/4)) + sqrt(n/2) + 2^(7/4)*n^(3/4)/3 - n) * n^(n - 1/8) / 2^(9/8) * (1 + 71323/(103680*2^(1/4)*n^(1/4))). - Vaclav Kotesovec, Dec 02 2021
MATHEMATICA
nmax = 20; CoefficientList[Series[E^(1/((1-x)*(1-x^2)*(1-x^3)) - 1), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Dec 02 2021 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(1/((1-x)*(1-x^2)*(1-x^3))-1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 25 2017
STATUS
approved