A204471 Number of 7-element subsets that can be chosen from {1,2,...,14*n+7} having element sum 49*n+28.

1, 3370, 108108, 957332, 4721127, 16627422, 47043624, 114106128, 246902225, 489197948, 903720482, 1576984058, 2624673317, 4197566692, 6488021194, 9736993054, 14241624013, 20363359008, 28536634496, 39278092476, 53196371385, 71002416300, 93520372350, 121698990952

Offset

0,2

Comments

a(n) is the number of partitions of 49*n+28 into 7 distinct parts <= 14*n+7.

Links

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

Formula

G.f.: -(94*x^21 +18950*x^20 +265472*x^19 +1391863*x^18 +4387222*x^17 +10120300*x^16 +18809933*x^15 +29668549*x^14 +40847915*x^13 +49820911*x^12 +54281003*x^11 +53032087*x^10 +46410392*x^9 +36173353*x^8 +24844747*x^7 +14749481*x^6 +7293277*x^5 +2809833*x^4 +741117*x^3 +101368*x^2 +3368*x+1) / ((x^2-x+1)*(x^4+x^3+x^2+x+1)*(x^2+1)*(x^2+x+1)^2*(x+1)^3*(x-1)^7).

Example

a(0) = 1 because there is 1 7-element subset that can be chosen from {1,2,...,7} having element sum 28: {1,2,3,4,5,6,7}.

Maple

a:= n-> (Matrix(22, (i, j)-> `if`(i=j-1, 1, `if`(i=22, [1, -2, 0, 1, 0, 1, -1, 2, -2, -1, 0, 0, 0, 1, 2, -2, 1, -1, 0, -1, 0, 2][j], 0)))^n. <<1, 3370, 108108, 957332, 4721127, 16627422, 47043624, 114106128, 246902225, 489197948, 903720482, 1576984058, 2624673317, 4197566692, 6488021194, 9736993054, 14241624013, 20363359008, 28536634496, 39278092476, 53196371385, 71002416300>>)[1, 1]: seq(a(n), n=0..50);

Crossrefs

Bisection of column k=7 of A204459.

Sequence in context: A014441 A293651 A212948 * A139778 A346025 A178506

Adjacent sequences: A204468 A204469 A204470 * A204472 A204473 A204474

Keyword

nonn,easy

Author

Alois P. Heinz, Jan 16 2012

Status

approved