3,2

With a different offset, number of n-permutations of 4 objects u, v, w, z with repetition allowed, containing exactly two u's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 29 2007

Numerators of sequence a[ 3, n ] in (b^2)[ i, j ]) where b[ i, j ] = binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.

a(n) = 3^(n-3)*binomial(n-1, 2); G.f.: (x/(1-3*x))^3. (Third convolution of A000244, powers of 3) - from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de).

a(n)=|A075513(n, 2)|/9, n>=3.

The sequence 0, 1, 9, 54, ... has e.g.f. exp(3x)(x+3x^2/2) - Paul Barry (pbarry(AT)wit.ie), Jul 23 2003

BB:=2^(n+3)*z^3/(2*z-3*z^2)^3: gser:=series(BB, z=0, 20): seq(coeff(gser, z, n), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 29 2007

seq(seq(binomial(i+1, j)*3^(i-1), j =i-1), i=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 29 2007

Cf. A027465.

Adjacent sequences: A027469 A027470 A027471 this_sequence A027473 A027474 A027475

Sequence in context: A059597 A023008 A079817 this_sequence A022637 A001392 A079764

nonn,easy

Olivier Gerard (ogerard(AT)ext.jussieu.fr)

Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006