A395483 - OEIS

%I #22 Apr 25 2026 15:43:53

%S 0,0,0,0,0,0,24,480,5984,57640,470504,3426320,22979920,144970904,

%T 872919960,5069777856,28621255872,157982891656,856443633608,

%U 4575819838960,24160867451824,126350618774264,655576175021944,3379581924222624,17329834154541600

%N Number of derangements of [n] with 4 descents.

%H Seiichi Manyama, <a href="/A395483/b395483.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (30,-400,3122,-15799,54176,-127512,203456,-210672,127872,-34560).

%F E.g.f.: 1024/3125 * exp(5*x) - 81*(1+4*x)/256 * exp(4*x) + 4*x*(2+3*x)/9 * exp(3*x) - x^2*(3+2*x)/6 * exp(2*x) - 81171/7200000 + 713*x/180000 - 9*x^2/4000 + x^3/150 + x^4/120.

%F G.f.: x^6 * (24-240*x+1184*x^2-4808*x^3+15520*x^4-31552*x^5+36864*x^6-24192*x^7+6912*x^8)/((1-2*x)^4 * (1-3*x)^3 * (1-4*x)^2 * (1-5*x)).

%F a(n) = 30*a(n-1) - 400*a(n-2) + 3122*a(n-3) - 15799*a(n-4) + 54176*a(n-5) - 127512*a(n-6) + 203456*a(n-7) - 210672*a(n-8) + 127872*a(n-9) - 34560*a(n-10) for n > 14.

%o (PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0], Vec(x^6*(24-240*x+1184*x^2-4808*x^3+15520*x^4-31552*x^5+36864*x^6-24192*x^7+6912*x^8)/((1-2*x)^4*(1-3*x)^3*(1-4*x)^2*(1-5*x))))

%Y Column k=4 of A219836.

%K nonn

%O 0,7

%A _Seiichi Manyama_, Apr 25 2026