A052521 Number of pairs of sequences of cardinality at least 3.

0, 0, 0, 0, 0, 0, 720, 10080, 120960, 1451520, 18144000, 239500800, 3353011200, 49816166400, 784604620800, 13076743680000, 230150688768000, 4268249137152000, 83230858174464000, 1703031405723648000

Offset

0,7

Links

G. C. Greubel, Table of n, a(n) for n = 0..445

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 88.

Formula

E.g.f.: x^6/(1-x)^2.

(n-5)*a(n+1) + (4 + 3*n - n^2)*a(n) = 0, with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = 0, a(6) = 720.

a(n) = (n-5)*n!.

From Amiram Eldar, Jan 14 2021: (Start)

Sum_{n>=6} 1/a(n) = 5477/7200 - 17*e/60 - gamma/120 + Ei(1)/120 = 5477/7200 - (17/60)*A001113 - (1/120)*A001620 + A091725/120.

Sum_{n>=6} (-1)^n/a(n) = 403/7200 - 1/(6*e) + gamma/120 - Ei(-1)/120 = 403/7200 - (1/6)*A068985 + (1/120)*A001620 + (1/120)*A099285. (End)

Maple

spec := [S, {B=Sequence(Z, 3 <= card), S=Prod(B, B)}, labeled]: # Pairs spec
seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

Table[If[n<6, 0, (n-5)*n!], {n, 0, 20}] (* G. C. Greubel, May 13 2019 *)

Prog

(PARI) {a(n) = if(n<6, 0, (n-5)*n!)}; \\ G. C. Greubel, May 13 2019
(Magma) [n le 5 select 0 else (n-5)*Factorial(n): n in [0..20]]; // G. C. Greubel, May 13 2019
(Sage) [0, 0, 0, 0, 0, 0]+[(n-5)*factorial(n) for n in (6..20)] # G. C. Greubel, May 13 2019
(GAP) Concatenation([0, 0, 0, 0, 0, 0], List([6..20], n-> (n-5)*Factorial(n))) # G. C. Greubel, May 13 2019

Crossrefs

Cf. sequences with formula (n + k)*n! listed in A282466.

Cf. A001113, A001620, A068985, A091725, A099285.

Sequence in context: A187192 A052792 A052790 * A213876 A052785 A052783

Adjacent sequences: A052518 A052519 A052520 * A052522 A052523 A052524

Keyword

nonn,easy

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved