A050930 Number of directed loopless multigraphs on 4 nodes with n arcs.

1, 1, 6, 20, 69, 196, 554, 1368, 3240, 7110, 14896, 29624, 56755, 104468, 186484, 322800, 544590, 896259, 1443834, 2278640, 3531647, 5380064, 8069672, 11926928, 17392983, 25042836, 35637168, 50152068, 69853604, 96344440, 131669538

Offset: 0

Author

Vladeta Jovovic, Dec 30 1999

Keywords

• easy
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=4 of A333361.

Cf. A037240.

Formula

G.f.: (2*x^18 + 9*x^17 + 20*x^16 + 46*x^15 + 98*x^14 + 133*x^13 + 196*x^12 + 226*x^11 + 254*x^10 + 240*x^9 + 207*x^8 + 128*x^7 + 92*x^6 + 43*x^5 + 24*x^4 + 8*x^3 + 2*x^2-x + 1)/((x^4-1)^3*(x^3-1)^4*(x^2-1)^3*(x-1)^2).