A260346 Expansion of x^2*((1 - 12*x + 50*x^2 - 76*x^3 + 42*x^4 - 48*x^5 + 32*x^6)/(1 - 4*x)^4 + 4*x^2/(1 - 4*x)^(5/2)).

0, 0, 1, 4, 22, 124, 706, 3968, 21880, 118192, 625776, 3251744, 16610072, 83537520, 414288080, 2028760544, 9822006896, 47063458528, 223408338400, 1051514839104, 4910856580376, 22772597352944, 104914684398352, 480457417780320, 2188115766353616, 9914318477830304, 44708936142838816

Offset: 0

Author

N. J. A. Sloane, Aug 02 2015

Keywords

• nonn

Links

• I. G. Enting and A. J. Guttmann, Area-weighted moments of convex polygons on the square lattice, J. Phys. A 22 (1989), 2639-2642. See Eq. (4).

Crossrefs

Cf. A005436.

Programs

Maple

t1:=x^2*( (1-12*x+50*x^2-76*x^3+42*x^4-48*x^5+32*x^6)/(1-4*x)^4 + 4*x^2/(1-4*x)^(5/2));
series(t1,x,40);
seriestolist(%);

Formula

G.f.: x^2*((1 - 12*x + 50*x^2 - 76*x^3 + 42*x^4 - 48*x^5 + 32*x^6)/(1 - 4*x)^4 + 4*x^2/(1 - 4*x)^(5/2)).