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A282085 Number of n-element subsets of [n+9] having an even sum. 2
1, 5, 25, 110, 365, 1001, 2485, 5720, 12190, 24310, 46126, 83980, 147070, 248710, 408430, 653752, 1021735, 1562275, 2343055, 3453450, 5008003, 7153575, 10079355, 14024400, 19284460, 26225628, 35302540, 47071640, 62203340, 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

FORMULA

G.f.: (x^2-x+1)*(x^8-4*x^7+20*x^6-36*x^5+54*x^4-36*x^3+20*x^2-4*x+1) / ((x^2+1)^5*(x-1)^10).

a(n) = A282011(n+9,n).

EXAMPLE

a(0) = 1: {}.

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

a(2) = 25: {1,3}, {1,5}, {1,7}, {1,9}, {1,11}, {2,4}, {2,6}, {2,8}, {2,10}, {3,5}, {3,7}, {3,9}, {3,11}, {4,6}, {4,8}, {4,10}, {5,7}, {5,9}, {5,11}, {6,8}, {6,10}, {7,9}, {7,11}, {8,10}, {9,11}.

MATHEMATICA

T[n_, k_] := Sum[Binomial[Ceiling[n/2], 2 j] Binomial[Floor[n/2], k - 2 j], {j, 0, Floor[(n + 1)/4]}]; Table[T[n + 9, n], {n, 0, 31}] (* or *) CoefficientList[Series[(x^2 - x + 1) (x^8 - 4 x^7 + 20 x^6 - 36 x^5 + 54 x^4 - 36 x^3 + 20 x^2 - 4 x + 1)/((x^2 + 1)^5 (x - 1)^10), {x, 0, 31}], x] (* Indranil Ghosh, Feb 26 2017 *)

CROSSREFS

Cf. A282011.

Sequence in context: A273828 A147161 A282077 * A290920 A267228 A183926

Adjacent sequences:  A282082 A282083 A282084 * A282086 A282087 A282088

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Feb 05 2017

STATUS

approved

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)