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A282077 Number of 9-element subsets of [n+9] having an even sum. 2
0, 5, 25, 110, 350, 1001, 2485, 5720, 12120, 24310, 46126, 83980, 146860, 248710, 408430, 653752, 1021240, 1562275, 2343055, 3453450, 5007002, 7153575, 10079355, 14024400, 19282640, 26225628, 35302540, 47071640, 62200280, 81505820, 105955628, 136719440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-5,-15,35,1,-65,45,45,-65,1,35,-15,-5,5,-1).

FORMULA

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

a(n) = ((384 + 400*n + 140*n^2 + 20*n^3 + n^4)*(-945*(-1+(-1)^n) + 3378*n + 1900*n^2 + 460*n^3 + 50*n^4 + 2*n^5)) / 1451520. - Colin Barker, Feb 06 2017

EXAMPLE

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

MATHEMATICA

LinearRecurrence[{5, -5, -15, 35, 1, -65, 45, 45, -65, 1, 35, -15, -5, 5, -1}, {0, 5, 25, 110, 350, 1001, 2485, 5720, 12120, 24310, 46126, 83980, 146860, 248710, 408430}, 40] (* Harvey P. Dale, Jun 10 2018 *)

PROG

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

CROSSREFS

Column k=9 of A282011.

Sequence in context: A275903 A273828 A147161 * A282085 A290920 A267228

Adjacent sequences:  A282074 A282075 A282076 * A282078 A282079 A282080

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Feb 05 2017

STATUS

approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)