A282078 Number of 10-element subsets of [n+10] having an even sum.

0, 5, 30, 140, 490, 1491, 3976, 9696, 21816, 46126, 92252, 176232, 323092, 571802, 980232, 1633984, 2655224, 4217499, 6560554, 10014004, 15021006, 22174581, 32253936, 46278336, 65560976, 91786604, 127089144, 174160784, 236361064, 317866884, 423822512

Offset: 0

Author

Alois P. Heinz, Feb 05 2017

Keywords

• nonn
• easy

Examples

			a(1) = 5: {1,2,3,4,5,6,7,8,9,11}, {1,2,3,4,5,6,7,9,10,11}, {1,2,3,4,5,7,8,9,10,11}, {1,2,3,5,6,7,8,9,10,11}, {1,3,4,5,6,7,8,9,10,11}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-10,-10,50,-34,-66,110,0,-110,66,34,-50,10,10,-6,1).

Crossrefs

Column k=10 of A282011.

Programs

PARI

concat(0, Vec(-x*(x^4+10*x^2+5)/((1+x)^5*(x-1)^11) + O(x^30))) \\ Colin Barker, Feb 06 2017

Formula

G.f.: -x*(x^4+10*x^2+5)/((1+x)^5*(x-1)^11).

a(n) = (-2735775*(-1+(-1)^n) - 45*(-344851 + 56595*(-1)^n)*n + (22908402-803250*(-1)^n)*n^2 - 50*(-325607+2079*(-1)^n)*n^3 + (6781885-4725*(-1)^n)*n^4 + 1802220*n^5 + 315546*n^6 + 36300*n^7 + 2640*n^8 + 110*n^9 + 2*n^10) / 14515200. - Colin Barker, Feb 06 2017