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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 279.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
Goulden, I. P.; Jackson, D. M.; Reilly, J. W.; The Hammond series of a symmetric function and its application to $P$-recursiveness. SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 179-193.
R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
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FORMULA
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E.g.f. f(x) = Sum_{n >= 0} a(2 * n) * x^n/(2 * n)! satisfies differential equation 6 * x^2 * ( - x^2 - 2 * x + 2) * diff(f(x), x, x) - (x^5 + 6 * x^4 + 6 * x^3 - 32 * x + 8) * diff(f(x), x) + x/6 * ( - x^2 - 2 * x + 2)^2 * f(x) = 0.
Recurrence: a(2 * n) = (2 * n)!/n! * v(n) where 48 * v(n) + ( - 72 * n^2 + 24 * n + 48) * v(n - 1) + (72 * n^3 - 432 * n^2 + 788 * n - 428) * v(n - 2) + (36 * n^4 - 324 * n^3 + 1052 * n^2 - 1428 * n + 664) * v(n - 3) + (36 * n^4 - 360 * n^3 + 1260 * n^2 - 1800 * n + 864) * v(n - 4) + (6 * n^5 - 94 * n^4 + 550 * n^3 - 1490 * n^2 + 1844 * n - 816) * v(n - 5) + ( - n^5 + 15 * n^4 - 85 * n^3 + 225 * n^2 - 274 * n + 120) * v(n - 6) = 0.
$\dsum\limits_{a_{2}=0}^{2n}\dsum\limits_{c=0}^{\min \{\lfloor (3n-a_{2})/3\rfloor ,\lfloor (2n-a_{2})/2\rfloor \}}\dsum\limits_{b=0}^{\min \{\lfloor (3n-a_{2}-3c)/2\rfloor ,\lfloor (2n-a_{2}-2c)/2\rfloor \}}\frac{% (-1)^{a_{2}+b}(2n)!(2\allowbreak (3n-a_{2}-2b-3c))!}{2^{(\allowbreak 5n-a_{2}-2b-4c)}3^{(2n-a_{2}-2b-c)}\allowbreak (3n-a_{2}-2b-3c)!a_{2}!b!c!(2n-a_{2}-2b-2c)!}$ [From Shanzhen Gao (sgao2(AT)fau.edu), Jun 05 2009]
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