OFFSET
0,4
COMMENTS
See Fig. 26, p. 1549 in the Cvitanovic reference. - Jonathan Vos Post, Feb 20 2010
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..368
P. Cvitanovic, Group theory for Feynman diagrams in non-Abelian gauge theories, Phys. Rev. D14 (1976), 1536-1553.
FORMULA
a(n) = Sum_{k=0..n-1} binomial(n-1, k) * a(k) * b(n-k) where b(1) = 0, b(2) = 1, b(n) = 2^(n-2) * (2*n-5)!! = A001813(n-2) [from Cvitanovic]. - Sean A. Irvine, Jun 17 2016
a(n) = Sum_{k=0..n-2} binomial(n-1, k) * ((2*n-2*k-4)!/(n-k-2)!) * a(k), with a(0) = 1. - G. C. Greubel, Nov 19 2022
MATHEMATICA
a[n_]:= a[n]= If[n==0, 1, Sum[Binomial[n-1, k]*((2*n-2*k-4)!/(n-k-2)!)*a[k], {k, 0, n-2}]];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Nov 19 2022 *)
PROG
(SageMath)
@CachedFunction
def a(n): # a = A005415
if (n==0): return 1
else: return sum(binomial(n-1, k)*factorial(n-k-2)*binomial(2*n-2*k-4, n-k-2)*a(k) for k in (0..n-2))
[a(n) for n in range(40)] # G. C. Greubel, Nov 19 2022
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Jun 17 2016
STATUS
approved