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A243877 Number of Dyck paths of semilength n having exactly 7 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)). 2

%I

%S 1,9,61,385,2323,13583,77363,430573,2348528,12584052,66372328,

%T 345160962,1772302098,8996192858,45189272314,224832198163,

%U 1108842335240,5424622033040,26340438937256,127018289627132,608569050945950,2898295732654434,13725710735084610

%N Number of Dyck paths of semilength n having exactly 7 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).

%H Alois P. Heinz, <a href="/A243877/b243877.txt">Table of n, a(n) for n = 29..400</a>

%p b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,

%p series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,

%p z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 8)))

%p end:

%p a:= n-> coeff(b(2*n, 0, 1), z, 7):

%p seq(a(n), n=29..60);

%Y Column k=7 of A243881.

%K nonn

%O 29,2

%A _Alois P. Heinz_, Jun 13 2014

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Last modified November 14 01:24 EST 2019. Contains 329108 sequences. (Running on oeis4.)