login
A052521
Number of pairs of sequences of cardinality at least 3.
3
0, 0, 0, 0, 0, 0, 720, 10080, 120960, 1451520, 18144000, 239500800, 3353011200, 49816166400, 784604620800, 13076743680000, 230150688768000, 4268249137152000, 83230858174464000, 1703031405723648000
OFFSET
0,7
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.
Sequence in context: A187192 A052792 A052790 * A213876 A052785 A052783
KEYWORD
nonn,easy
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved