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Sum from {k=1} to {n} C(n+1, k-1)C(n+1, k)C(n+1, k+1) / C(n+1, 1)C(n+1, 2).

(n + 1)*(n + 2)*(n + 3)*(3*n - 2)*a(n) = 2*(n + 1)*(9*n^3 + 3*n^2 - 4*n + 4)*a(n - 1) + (3*n - 1)*(n - 2)*(15*n^2 - 5*n - 14)*a(n - 2) + 8*(3*n + 1)*(n - 2)^2*(n - 3)*a(n - 3), n>1.

(n+2)(n+3)a(n) = (7n^2+7n-2)*a(n-1) + 8(n-1)(n-2)a(n-2); a(0)=a(1)=1 - Richard L. Ollerton (r.ollerton(AT)uws.edu.au), Sep 13 2006

a(4)=22 since all permutations of length 4 are Baxter except 2413 and 3142.

C := binomial; A001181 := proc(n) local k; add(C(n+1, k-1)*C(n+1, k)*C(n+1, k+1)/(C(n+1, 1)*C(n+1, 2)), k=1..n); end;

A001181[n_]:=HypergeometricPFQ[{-1-n, -n, 1-n}, {2, 3}, -1] (* n>0 *) - Richard L. Ollerton (r.ollerton(AT)uws.edu.au), Sep 13 2006

(PARI) alias(C, binomial); a(n)=if(n<0, 0, sum(k=1, n, C(n+1, k-1)*C(n+1, k)*C(n+1, k+1)/C(n+1, 1)/C(n+1, 2)))

Cf. A001183, A001185, A046996.

Sequence in context: A089449 A124293 A107591 this_sequence A130579 A107945 A014330

Adjacent sequences: A001178 A001179 A001180 this_sequence A001182 A001183 A001184

nonn,nice,easy

njas, Simon Plouffe (plouffe(AT)math.uqam.ca)

Additional comments from Michael Somos, Jul 19 2002.