A395483 Number of derangements of [n] with 4 descents.

0, 0, 0, 0, 0, 0, 24, 480, 5984, 57640, 470504, 3426320, 22979920, 144970904, 872919960, 5069777856, 28621255872, 157982891656, 856443633608, 4575819838960, 24160867451824, 126350618774264, 655576175021944, 3379581924222624, 17329834154541600

Offset

0,7

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (30,-400,3122,-15799,54176,-127512,203456,-210672,127872,-34560).

Formula

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.

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)).

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.

Prog

(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))))

Crossrefs

Column k=4 of A219836.

Sequence in context: A263476 A263470 A276816 * A200979 A361576 A052715

Adjacent sequences: A395480 A395481 A395482 * A395484 A395485 A395486

Keyword

nonn

Author

Seiichi Manyama, Apr 25 2026

Status

approved