
REFERENCES

R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


PROG

(PARI)
dpermcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i1], k+1, 1); m*=2*t*k; s+=2*t); s!/m}
S(n, x)={vector(n, n, if(n>1, sum(k=0, n, binomial(2*nk, k)*2*n/(2*nk)*x^k), 0))}
q(n, s)={my(t=0); if(n>1, forpart(p=n, t+=dpermcount(p)*prod(i=1, #p, s[p[i]]), [2, n])); t}
a(n)={my(p=q(n, S(n, x))); sum(i=0, poldegree(p), polcoeff(p, ni)*(1)^(ni)*(2*i)!/(2^i*i!))} \\ Andrew Howroyd, Dec 18 2017
