OFFSET
0,2
LINKS
Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(n) = (n-1)!*Sum_{i=0..n-1} binomial(n+i,n-i-1)*n^i/i!. - corrected by Vaclav Kotesovec, Jan 26 2014
a(n) ~ c * n^n * ( exp(m-1) * (1+m)^(1+m) / (m^(3*m) * 2^(2*m) * (1-m)^(1-m)) )^n, where m = 1/12*(-1 + (215 - 12*sqrt(321))^(1/3) + (215 + 12*sqrt(321))^(1/3)) = 0.5566930950324... is the root of the equation m^2*(1+4*m)=1, and c = 2.194433179699246977948075450550764549... - Vaclav Kotesovec, Jan 26 2014
MATHEMATICA
a[n_] := (n+1)!*HypergeometricPFQ[ {-n, n+2}, {1, 3/2}, -(n+1)/4]; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Mar 01 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Dec 29 2010
STATUS
approved