A217525 From the enumeration of involutions avoiding the pattern 4321.

0, 0, 0, 0, 0, 2, 4, 6, 15, 31, 67, 155, 343, 787, 1829, 4233, 9940, 23454, 55540, 132390, 316704, 760462, 1833050, 4431552, 10745282, 26125316, 63672044, 155536070, 380739734, 933832952, 2294581836, 5647750518, 13923153431, 34375447863, 84989987987, 210407135915, 521547749731, 1294310608775, 3215632551785, 7997467696213, 19910095233857

Offset

0,6

Links

Table of n, a(n) for n=0..40.

Piera Manara and Claudio Perelli Cippo, The fine structure of 4321 avoiding involutions and 321 avoiding involutions, PU. M. A. Vol. 22 (2011), 227-238; See Theorem 4.2.

Formula

Manara and Cippo give a g.f.

Maple

A217525 := proc(nmax)
    local x ;
    -4+4/(1+x^2)+1/(1+x)^2 ;
    1/(1+x)-2*x^2*(1+x)-sqrt(%) ;
    taylor(%/2, x=0, nmax+1) ;
    seq(coeftayl(%, x=0, n), n=0..nmax) ;
end proc: # R. J. Mathar, Nov 05 2012

Mathematica

a[n_] := SeriesCoefficient[(1/2)(-2(x+1)x^2 - Sqrt[4/(x^2+1) + 1/(x+1)^2 - 4] + 1/(x+1)), {x, 0, n}];
a /@ Range[0, 40] (* Jean-François Alcover, Apr 04 2020 *)

Crossrefs

Sequence in context: A349979 A192536 A227902 * A295615 A127679 A049022

Adjacent sequences: A217522 A217523 A217524 * A217526 A217527 A217528

Keyword

nonn

Author

N. J. A. Sloane, Oct 13 2012

Status

approved