0,4

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.

R. W. Robinson, Table of n, a(n) for n = 0..30

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.

A diagonal of A059441. Cf. A005814.

Sequence in context: A103157 A007099 A004109 this_sequence A005983 A014608 A075405

Adjacent sequences: A002826 A002827 A002828 this_sequence A002830 A002831 A002832

nonn

njas

More terms and formula from Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 25 2001