OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..160
I. P. Goulden and D. M. Jackson, Labelled graphs with small vertex degrees and P-recursiveness, SIAM J. Algebraic Discrete Methods 7(1986), no. 1, 60--66. MR0819706 (87k:05093).
FORMULA
See Goulden-Jackson for the e.g.f.
Recurrence (for n>5): 3*a(n) = 3*(2*n - 1)*(3*n^2 - 3*n + 1)*a(n-1) + 3*(n-1)*(2*n - 3)*(2*n - 1)*(10*n + 7)*a(n-2) - 2*(n-2)*(n-1)*(2*n - 5)*(2*n - 3)*(2*n - 1)*(3*n + 4)*a(n-3) + 2*(n-3)*(n-2)*(n+1)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4). - Vaclav Kotesovec, Sep 15 2014
a(n) ~ sqrt(2) * 6^n * n^(3*n) / exp(3*n-4). - Vaclav Kotesovec, Sep 15 2014
MATHEMATICA
max=30; f[x_]:=Sum[a[n]*(x^n/n!), {n, 0, max}]; a[0]=1; a[1]=5; coef = CoefficientList[9*x^3*(x^4 - 4*x^2 - 2)*f''[x] - 3*(x^10 - 14*x^8 + 41*x^6 + 36*x^4 + 2*x^2 - 8)*f'[x] + x*(x^10 - 18*x^8 + 120*x^6 - 272*x^4 - 324*x^2 - 120)*f[x], x]; Table[a[n], {n, 0, max, 2}]/.Solve[Thread[coef[[2;; max]]==0]][[1]] (* Vaclav Kotesovec, Sep 15 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 02 2013
EXTENSIONS
More terms from Vaclav Kotesovec, Sep 15 2014
STATUS
approved