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A052520
Number of pairs of sequences of cardinality at least 2.
4
0, 0, 0, 0, 24, 240, 2160, 20160, 201600, 2177280, 25401600, 319334400, 4311014400, 62270208000, 958961203200, 15692092416000, 271996268544000, 4979623993344000, 96035605585920000, 1946321606541312000
OFFSET
0,5
FORMULA
E.g.f.: x^4/(1-x)^2.
(n-3)*a(n+1) + (2+n-n^2)*a(n) = 0, with a(0) = a(1) = a(2) = a(3) = 0, a(4) = 24.
a(n) = (n-3)*n!, n>2.
a(n) = (n+1)!*(n-3)/(n+1), n>2. - Gary Detlefs, Oct 02 2011
From Amiram Eldar, Jan 14 2021: (Start)
Sum_{n>=4} 1/a(n) = 59/36 - 2*e/3 - gamma/6 + Ei(1)/6 = 59/36 - (2/3)*A001113 - (1/6)*A001620 + A091725/2.
Sum_{n>=4} (-1)^n/a(n) = 1/36 - 1/(3*e) + gamma/6 - Ei(-1)/6 = 1/36 - (1/3)*A068985 + (1/6)*A001620 + (1/6)*A099285. (End)
MAPLE
Pairs spec := [S, {B=Sequence(Z, 2 <= card), S=Prod(B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
Table[Sum[n!, {i, 4, n}], {n, 0, 19}] (* Zerinvary Lajos, Jul 12 2009 *)
With[{nn=20}, CoefficientList[Series[x^4/(x-1)^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 03 2016 *)
PROG
(PARI) {a(n) = if(n<4, 0, (n-3)*n!)}; \\ G. C. Greubel, May 13 2019
(Magma) [n le 3 select 0 else (n-3)*Factorial(n): n in [0..20]]; // G. C. Greubel, May 13 2019
(Sage) [0, 0, 0, 0]+[(n-3)*factorial(n) for n in (4..20)] # G. C. Greubel, May 13 2019
(GAP) Concatenation([0, 0, 0, 0], List([4..20], n-> (n-3)*Factorial(n))) # G. C. Greubel, May 13 2019
CROSSREFS
Cf. sequences with formula (n + k)*n! listed in A282466.
Sequence in context: A052753 A353358 A353119 * A052724 A357242 A000536
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved