4,1

I have derived the terms in a rather laborius way (see the Maple program), following the Haight paper, where the signed sequence occurs. The simple g.f. for the positive sequence is conjectured by analogy with A006043. For the signed sequence it is, obviously, 6x^4/(1+4x)^4. The Maple program, probably not the simplest one, is for the signed sequence. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2004

Fourth column of triangle A152818 (1,1,1,1,4,2,1,12,) or A152818(9),A152818(13),A152818(18),A152818(24),A152818(31),. See submitted A153027. Linked to factorial polynomials A152650/A152656 (also not simplified A009998/A119502, correct in it bad value A119052). [From Paul Curtz (bpcrtz(AT)free.fr), Dec 17 2008]

Column 3 of square array A152818. [From Omar E. Pol (info(AT)polprimos.com), Jan 07 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

F. A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424.

It seems that G.f.= 6x^4/(1-4x)^4 (for the positive sequence). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2004

a(n) = 4^(n-4)*(n-3)*(n-2)*(n-1). [From Omar E. Pol (info(AT)polprimos.com), Jan 04 2009] E.g. a(6)=960 because 4^(6-4)*(6-3)*(6-2)*(6-1) = 4^2*3*4*5 = 16*3*4*5 = 960. [From Omar E. Pol (info(AT)polprimos.com), Jan 04 2009]

a(n) = 4^(n-4)*(n-1)!/(n-4)!. [From Omar E. Pol (info(AT)polprimos.com), Jan 15 2009]

A:=(u, r)->r*u^(u-r-1)/(u-r)!: a:=proc(i, j) if j>i+1 then 0 elif j=i+1 then 1 else A(z-j+1, z-i) fi end: with(linalg): B:=proc(z, x) if z=x then 1 else (-1)^(z+x)*det(matrix(z-x, z-x, a)) fi end: seq(expand(subs(z=k, (z-1)!*B(k, 4))), k=4..26);

Cf. A152818. [From Omar E. Pol (info(AT)polprimos.com), Jan 05 2009]

Cf. A000142, A006043, A152818, A154120. [From Omar E. Pol (info(AT)polprimos.com), Jan 15 2009]

Sequence in context: A115400 A055358 A030989 this_sequence A001805 A139743 A156460

Adjacent sequences: A006041 A006042 A006043 this_sequence A006045 A006046 A006047

sign

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 29 2004