A060517 Triangle T(n,k) of series-reduced (or homeomorphically irreducible) graphs with loops on n labeled nodes and with k edges, k=0..binomial(n+1,2).

1, 1, 0, 1, 1, 2, 1, 1, 3, 6, 6, 6, 3, 1, 1, 6, 15, 34, 58, 60, 60, 50, 33, 10, 1, 1, 10, 35, 120, 265, 475, 820, 1200, 1615, 1860, 1693, 1060, 425, 105, 15, 1, 1, 15, 75, 330, 990, 2691, 6326, 13170, 26205, 48055, 79206, 112863, 133535, 124680, 88890, 47874

Offset: 0

Author

Vladeta Jovovic, Mar 24 2001

Keywords

• easy
• nonn
• tabf

Examples

			[1], [1, 0], [1, 1, 2, 1], [1, 3, 6, 6, 6, 3, 1], [1, 6, 15, 34, 58, 60, 60, 50, 33, 10, 1], [1, 10, 35, 120, 265, 475, 820, 1200, 1615, 1860, 1693, 1060, 425, 105, 15, 1], [1, 15, 75, 330, 990, 2691, 6326, 13170, 26205, 48055, 79206, 112863, 133535, 124680, 88890, 47874, 19443, 5925, 1330, 210, 21, 1], ...
		

References

• I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.

Crossrefs

Row sums: A060516, A003514, A060514.

Formula

E.g.f.: (1 + x * y)^( - 1/2) * exp( - x * y/2 - x^2 * y^2/4) * Sum_{k=0..inf}(1 + x)^binomial(k + 1, 2) * exp( - x^2 * y * k^2/(2 * (1 + x * y)) + x^2 * y * k/2) * x^k/k!