1,2

a(n) is equal to the number of functions f:{1,2,3,4}->{1,2,...,n} such that for fixed different x_1, x_2 in {1,2,3,4} and fixed y_1, y_2 in {1,2,...,n} we have f(x_1)<>y_1 and f(x_2)<>y_2. - Milan R. Janjic (agnus(AT)blic.net), Apr 17 2007

a(n+1)=4, A061038(1), A061040(1), A061042(1), A061044(1), A061046(1), A061048(1), A061050(1);after 4 (which is linked to Lyman by "companion" of A005563, A000290(n+1)?), from Balmer, Paschen, Brackett, Pfund, Humphreys, Hansen-Strong, .., s-th spectra of hydrogen. Corresponding numerators or "companions" are A144396. [From Paul Curtz (bpcrtz(AT)free.fr), Nov 05 2008]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 21 2009: (Start)

The third differences of certain values of the hypergeometric function 3F2 lead to this sequence i.e. 3F2([1,n+1,n+1], [n+2,n+2], z=1) - 3*3F2([1,n+2,n+2], [n+3,n+3], z=1) + 3*3F2([1,n+3,n+3], [n+4,n+4], z=1) - 3F2([1,n+4,n+4], [n+5,n+5], z=1) = (1/((n+2)*(n+3)))^2 with n = -1, 0, 1,2, .. . See also A162990.

(End)

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Wolfram Research, Hypergeometric Function 3F2, The Wolfram Functions site. [From Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 21 2009]

Diagonal of [A132710]*Transpose[A132710]. - Tom Copeland (tcjpn(AT)msn.com), Nov 20 2007

a(n) = n^2 (n-1)^2

a(n) = A002378(n)^2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 11 2006

Contribution from Stephen Crowley (crow(AT)crowlogic.net), Jul 19 2009: (Start)

a(n)=limit(n!*(2*n+1)/(diff(1+polylog(2,x)-polylog(2,x)/x, x$n),x=0) and int(1+polylog(2,x)-polylog(2,x)/x,x=0..1)=Zeta(2)-Zeta(3)

sum((n^2*(n-1)^2)^(-1),n=2..infinity)=2*Zeta(2)-3 (End)

seq((numbperm (n, 2))^2, n=1..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2007

a:=n->sum(sum(n^2, j=0..n), k=0..n): seq(a(n), n=0..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007

a:=n->sum(sum (2*binomial(n, 2), j=2..n), k=1..n): seq(a(n), n=1..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007

map(f->if(f=0, 0, denom(f)), PolynomialTools[CoefficientList](convert(series(1+polylog(2, x)-polylog(2, x)/x, x, 20), polynom), x)) [From Stephen Crowley (crow(AT)crowlogic.net), Jul 19 2009]

lst={}; Do[s0=n^2; s1=(n+1)^2; AppendTo[lst, s1*s0], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 19 2009]

(Other) sage: [n^2*(n-1)^2 for n in xrange(1, 35)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 03 2009]

Cf. A002378.

Sequence in context: A045490 A060783 A125756 this_sequence A083223 A102263 A103931

Adjacent sequences: A035284 A035285 A035286 this_sequence A035288 A035289 A035290

nonn,new

Erich Friedman (erich.friedman(AT)stetson.edu)