A007345 Number of Havender tableaux of height 2 with n columns. (Formerly M3575)

1, 4, 21, 127, 831, 5722, 40879, 300440, 2258455, 17291704, 134417955, 1058279251, 8422155293, 67647554826, 547699155261, 4465275681735, 36627214297455, 302067234113560, 2503174651819435, 20832888975309257, 174057811108059017, 1459365504991034106

Offset

0,2

References

D. Gouyou-Beauchamps, "Tableaux de Havender standards," in S. Brlek, editor, Parallélisme: Modèles et Complexité. LACIM, Université du Québec à Montréal, 1989.

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

D. Gouyou-Beauchamps, Tableaux de Havender standards, Parallélisme: Modèles et Complexité. LACIM, Université du Québec à Montréal, 1989. (Annotated scanned copy)

Formula

G.f.: (sqrt(1-5*x^2) - sqrt(1-9*x^2)) / (2 * x^2 * sqrt(1-x^2)) [from Gouyou-Beauchamps]. - Sean A. Irvine, Dec 28 2017

a(n) = Sum_{q=0..2*n} Sum_{j=max(0, n-q)..floor((2*n-q)/2)} n! * (4*n-2*q-2*j)! / ((2*n-q-2*j)! * (j+1)! * ((2*n-q-j)!)^2 * (q-n+j)!) [from Gouyou-Beauchamps]. - Sean A. Irvine, Dec 28 2017

Crossrefs

Row sums of A259992.

Sequence in context: A353608 A032326 A281581 * A255673 A099250 A293192

Adjacent sequences: A007342 A007343 A007344 * A007346 A007347 A007348

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from Sean A. Irvine, Dec 28 2017

Status

approved