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A322782 Number of lattice paths from {2}^n to {0}^n using steps that decrement one component by 1 such that for each point (p_1,p_2,...,p_n) we have abs(p_{i}-p_{i+1}) <= 1 and abs(p_{1}-p_{n}) <= 1. 1
1, 1, 4, 36, 720, 23400, 1123200, 74440800, 6509318400, 725829724800, 100511918784000, 16922530756454400, 3404178048774758400, 806369627582929612800, 222159405758654317363200, 70435689828806256514560000, 25463217531292911649057996800, 10411540182139235537714555289600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = n * A318191(2,n) for n > 0. - Alois P. Heinz, Jan 09 2019

MAPLE

b:= proc(l) option remember; (n-> `if`(n<2 or max(l[])=0, 1,

      add(`if`(l[i]=0 or 1<abs(l[`if`(i=1, 0, i)-1]-l[i]+1)

                      or 1<abs(l[`if`(i=n, 0, i)+1]-l[i]+1), 0,

        b(subsop(i=l[i]-1, l))), i=1..n)))(nops(l))

    end:

a:= n-> b([2$n]):

seq(a(n), n=0..12);  # Alois P. Heinz, Jan 05 2019

CROSSREFS

Cf. A227656, A318191.

Sequence in context: A163887 A156630 A289545 * A145565 A214669 A126152

Adjacent sequences:  A322779 A322780 A322781 * A322783 A322784 A322785

KEYWORD

nonn,walk

AUTHOR

Woong-Gi Jung, Dec 26 2018

EXTENSIONS

More terms from Alois P. Heinz, Dec 30 2018

STATUS

approved

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Last modified September 15 16:40 EDT 2019. Contains 327078 sequences. (Running on oeis4.)