A214436 The number of up-up-down permutations of Z(4n-1).

2, 132, 84512, 223951392, 1685183094272, 28969792974769152, 987034310041026732032, 60293392724182748896038912, 6128851480537130997344765345792, 978655905392130555745715195271708672, 234471526233667759898500618954899615383552, 81191298195592060653451439857277800300708626432

Offset

1,1

Comments

The equation in Theorem 3.2 of the paper contains a typographical index error: The correct denominator in the e.g.f. is phi_0(x)^2-phi_1(x)*phi_3(x), equivalent to eq. (3.14).

Links

Table of n, a(n) for n=1..12.

L. Carlitz and Richard Scoville, Enumeration of rises and falls by position, Discr. Math. 5 (1973) 45-59, variable B(4n-1).

Maple

Ph := proc(i, x)
        local n;
        add( x^(4*n+i)/(4*n+i)!, n=0..90) ;
end proc:
g := (Ph(1, x)*Ph(2, x)-Ph(0, x)*Ph(3, x) ) / (Ph(0, x)^2-Ph(1, x)*Ph(3, x)) ;
for n from 3 to 29 by 4 do
        coeftayl(g, x=0, n)*n! ;
end do;

Mathematica

Ph[i_, x_] = Sum[x^(4*n + i)/(4*n + i)!, {n, 0, Infinity}];
g = (Ph[1, x]*Ph[2, x]-Ph[0, x]*Ph[3, x]) / (Ph[0, x]^2-Ph[1, x]*Ph[3, x]);
a[n_] := SeriesCoefficient[g, {x, 0, 4 n - 1}]*(4 n - 1)!;
Table[a[n], {n, 1, 12}] (* Jean-François Alcover, May 28 2024, after R. J. Mathar *)

Crossrefs

Sequence in context: A174585 A186194 A099682 * A135759 A014315 A221468

Adjacent sequences: A214433 A214434 A214435 * A214437 A214438 A214439

Keyword

nonn

Author

R. J. Mathar, Jul 17 2012

Status

approved