A395482 Number of derangements of [n] with 3 descents.

0, 0, 0, 0, 1, 12, 120, 896, 5544, 30384, 153400, 731040, 3341256, 14806544, 64107096, 272697216, 1144354792, 4752083952, 19573444728, 80110516064, 326251853832, 1323504508368, 5352686795416, 21596226671424, 86969629500456, 349717233298352, 1404638031773880

Offset

0,6

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-105,362,-692,696,-288).

Formula

E.g.f.: 81/256 * exp(4*x) - 8*(1+3*x)/27 * exp(3*x) + x*(1+x)/2 * exp(2*x) - 139/6912 + 7*x/576 - x^2/32 - x^3/24.

G.f.: x^4 * (1-4*x+33*x^2-126*x^3+156*x^4-72*x^5)/((1-2*x)^3 * (1-3*x)^2 * (1-4*x)).

a(n) = 16*a(n-1) - 105*a(n-2) + 362*a(n-3) - 692*a(n-4) + 696*a(n-5) - 288*a(n-6) for n > 9.

Prog

(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(x^4*(1-4*x+33*x^2-126*x^3+156*x^4-72*x^5)/((1-2*x)^3*(1-3*x)^2*(1-4*x))))

Crossrefs

Column k=3 of A219836.

Sequence in context: A009050 A067358 A268634 * A061506 A059155 A012443

Adjacent sequences: A395479 A395480 A395481 * A395483 A395484 A395485

Keyword

nonn

Author

Seiichi Manyama, Apr 25 2026

Status

approved