A112504 - OEIS

%I #13 Jul 10 2025 19:39:55

%S 1,35,665,9107,100751,957197,8110087,62854845,453710670,3091406010,

%T 20086835910,125465290530,758173316850,4455503465430,25571494599330,

%U 143839855533270,795332428661055,4333564250230845,23317657891319095

%N Fifth column of triangle A112500.

%C For a combinatorial formula see A112500, case k=5.

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (35, -560, 5432, -35714, 168542, -589632, 1556776, -3126949, 4777591, -5506936, 4703032, -2881136, 1195632, -300672, 34560).

%F G.f.: 1/product((1-j*x)^(6-j), j=1..5) = 1/(((1-x)^5)*((1-2*x)^4)*((1-3*x)^3)*((1-4*x)^2)*(1-5*x)).

%F a(n) computable from partial fraction decomposition of g.f. Cf. A112503.

%t CoefficientList[Series[1/Product[(1-j*x)^(6-j),{j,1,5}],{x,0,20}],x] (* _Georg Fischer_, Jul 10 2025 *)

%Y Cf. A112500, A112502, A112503.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 14 2005