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 A005415 Number of simple tensors with n external gluons. (Formerly M2080) 1
 1, 0, 1, 2, 15, 140, 1915, 33810, 734545, 18929960, 564216345, 19088149850, 722508543295, 30249199720740, 1387823333771875, 69238799231051450, 3731906171773805025, 216101966957781304400, 13379538319131196637425, 881962125004262056604850 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A001813. Sequence in context: A285449 A371584 A288950 * A371523 A219868 A224885 Adjacent sequences: A005412 A005413 A005414 * A005416 A005417 A005418 KEYWORD nonn,nice AUTHOR N. J. A. Sloane EXTENSIONS More terms from Sean A. Irvine, Jun 17 2016 STATUS approved

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Last modified June 23 21:27 EDT 2024. Contains 373654 sequences. (Running on oeis4.)