OFFSET
0,3
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 10, R_p.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.20, G(x).
LINKS
T. D. Noe, Table of n, a(n) for n=0..50
FORMULA
E.g.f.: (Sum_{n>1} 2^binomial(n, 2)*x^n/(n-1)!)/(Sum_{n>=0} 2^binomial(n, 2)*x^n/n!).
a(n) = n * A001187(n).
MAPLE
add(2^binomial(n, 2)*x^n/(n-1)!, n=1..31)/add(2^binomial(n, 2)*x^n/n!, n=0..31);
MATHEMATICA
f[x_, lim_] := Sum[2^Binomial[n, 2]*x^n/(n - 1)!, {n, 1, lim}] / Sum[2^Binomial[n, 2]*x^n/n!, {n, 0, lim}]; nn = 15; Range[0, nn]! CoefficientList[Series[f[x, nn], {x, 0, nn}], x] (* T. D. Noe, Oct 21 2011 *)
PROG
(PARI) q=30; my(x='x+O('x^20)); concat([0], Vec(serlaplace( sum(j=1, q, 2^binomial(j, 2)*x^j/(j-1)!)/(sum(k=0, q, 2^binomial(k, 2)*x^k/k!)) ))) \\ G. C. Greubel, May 16 2019
(Magma) q:=30; m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (&+[2^Binomial(j, 2)*x^j/Factorial(j-1): j in [1..q]])/(&+[2^Binomial(k, 2)*x^k/Factorial(k):k in [0..q]]) )); [0] cat [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, May 16 2019
(Sage) q=30; m = 20; T = taylor(sum(2^binomial(j, 2)*x^j/factorial(j-1) for j in (1..q))/(sum(2^binomial(k, 2)*x^k/factorial(k) for k in (0..q))), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 16 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 16 2000
STATUS
approved