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

%I #13 Oct 31 2018 17:03:19

%S 1,3370,108108,957332,4721127,16627422,47043624,114106128,246902225,

%T 489197948,903720482,1576984058,2624673317,4197566692,6488021194,

%U 9736993054,14241624013,20363359008,28536634496,39278092476,53196371385,71002416300,93520372350,121698990952

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

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

%H Alois P. Heinz, <a href="/A204471/b204471.txt">Table of n, a(n) for n = 0..1000</a>

%F 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).

%e 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}.

%p 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);

%Y Bisection of column k=7 of A204459.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Jan 16 2012

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Last modified November 30 21:14 EST 2023. Contains 367462 sequences. (Running on oeis4.)