OFFSET
1,3
FORMULA
a(n)=(sum(k=0..n-1, (n+k-1)!*sum(j=0..k, (-1)^j/(k-j)!*sum(i=0..min(j,(n+j-1)/3),(1/i!)*(-1)^i* stirling1(n-3*i+j-1,j-i)/(3^i*(n-3*i+j-1)!))))), n>0.
a(n) ~ n^(n-1) / (sqrt(s*(2+s^3)) * exp(n) * r^(n-1/2)), where s = 1/3*(-1 + (25/2 - (3*sqrt(69))/2)^(1/3) + (1/2*(25 + 3*sqrt(69)))^(1/3)) = 0.75487766624669276... is the root of the equation s^2*(1+s) = 1 and r = log(1+s) - s^3/3 = 0.4190125789786... - Vaclav Kotesovec, Jan 22 2014
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[Log[1+x]-x^3/3, {x, 0, 20}], x], x]*Range[0, 20]!] (* Vaclav Kotesovec, Jan 22 2014 *)
PROG
(Maxima) a(n):=(sum((n+k-1)!*sum((-1)^j/(k-j)!*sum((1/i!)*(-1)^i*stirling1(n-3*i+j-1, j-i)/(3^i*(n-3*i+j-1)!), i, 0, min(j, (n+j-1)/3)), j, 0, k), k, 0, n-1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Feb 07 2012
STATUS
approved