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A243880
Number of Dyck paths of semilength n having exactly 10 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)).
2
1, 12, 100, 749, 5281, 35641, 232123, 1466180, 9017295, 54172152, 318732558, 1840668348, 10452539055, 58458147585, 322425939233, 1755834940554, 9450381436619, 50317234401194, 265235076809408, 1385156654929038, 7171253075566076, 36826968212298201
OFFSET
41,2
LINKS
MAPLE
b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,
series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,
z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 11)))
end:
a:= n-> coeff(b(2*n, 0, 1), z, 10):
seq(a(n), n=41..70);
CROSSREFS
Column k=10 of A243881.
Sequence in context: A358302 A085374 A016283 * A338811 A199681 A211403
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 13 2014
STATUS
approved