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A282078
Number of 10-element subsets of [n+10] having an even sum.
2
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
0,2
LINKS
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).
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
EXAMPLE
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}.
PROG
(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
CROSSREFS
Column k=10 of A282011.
Sequence in context: A213260 A054612 A358543 * A080951 A375253 A359094
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Feb 05 2017
STATUS
approved