A204469 Number of 5-element subsets that can be chosen from {1,2,...,10*n+5} having element sum 25*n+15.

1, 141, 1394, 5910, 17053, 39361, 78602, 141702, 236833, 373309, 561704, 813722, 1142341, 1561651, 2087034, 2734970, 3523243, 4470721, 5597592, 6925112, 8475873, 10273519, 12343044, 14710482, 17403231, 20449711, 23879724, 27724080, 32014983, 36785631, 42070632

Offset

0,2

Comments

a(n) is the number of partitions of 25*n+15 into 5 distinct parts <= 10*n+5.

Links

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

Formula

G.f.: -(12*x^10 +390*x^9 +1821*x^8 +4057*x^7 +6070*x^6 +6651*x^5 +5374*x^4 +3123*x^3 +1112*x^2 +139*x+1) / ((x^2+x+1)*(x^2+1)*(x+1)^2*(x-1)^5).

Example

a(0) = 1 because there is 1 5-element subset that can be chosen from {1,2,3,4,5} having element sum 15: {1,2,3,4,5}.

Maple

a:= n-> (Matrix(11, (i, j)-> `if`(i=j-1, 1, `if`(i=11, [1, -2, 0, 1, 0, 2, -2, 0, -1, 0, 2][j], 0)))^n. <<1, 141, 1394, 5910, 17053, 39361, 78602, 141702, 236833, 373309, 561704>>)[1, 1]: seq(a(n), n=0..50);

Crossrefs

Bisection of column k=5 of A204459.

Sequence in context: A235760 A201814 A235543 * A201553 A281560 A186955

Adjacent sequences: A204466 A204467 A204468 * A204470 A204471 A204472

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 16 2012

Status

approved