OFFSET
0,2
REFERENCES
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.82).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..210
Yiyang Jia and Jacobus J. M. Verbaarschot, Large N expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs, arXiv:1806.03271 [hep-th], 2018.
Yiyang Jia and Jacobus J. M. Verbaarschot, Large N expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs, J. High Energ. Phys. (2018) 2018: 31.
L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10, esp. Eq. (16).
FORMULA
G.f.: REVERT(x/cosh(x)) = Sum_{n>=0} a(n)*x^(2n+1)/(2n+1)!. - Paul D. Hanna, Oct 15 2003
a(n) = (1/2^(2*n+1)) * Sum_{k=0..2*n+1} binomial(2*n+1, k)*(2*k-2*n-1)^(2*n).
MAPLE
[ seq((1/2^(2*n+1))*add( binomial(2*n+1, j)*(2*j-(2*n+1))^(2*n), j=0..(2*n+1)), n=1..30) ];
MATHEMATICA
Table[1/2^(2n+1) Sum[Binomial[2n+1, k](2k-2n-1)^(2n), {k, 0, 2n+1}], {n, 0, 20}] (* Harvey P. Dale, Mar 06 2012 *)
PROG
(PARI) a(n)=local(X); if(n<0, 0, X=x+O(x^(2*n+1)); (2*n+1)!*polcoeff(serreverse(x/cosh(x)), 2*n+1)) \\ Paul D. Hanna, Oct 15 2003
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
EXTENSIONS
Edited by Christian G. Bower, Jan 13 2004
STATUS
approved