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 A175137 Irregular triangle T(n,k) read by rows: number of orbits of size 2^k on Dyck n-paths. 0
 1, 2, 3, 1, 6, 2, 1, 12, 7, 4, 26, 23, 11, 2, 59, 71, 41, 8, 138, 224, 151, 30, 332, 709, 550, 114, 814, 2253, 1993, 406, 16, 2028, 7189, 7211, 1564, 64, 5118, 23045, 26221, 6010, 240, 13054, 74213, 95583, 23062, 912, 33598, 239979, 349145, 88530, 3504, 87143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..52. David Callan, A bijection on Dyck paths and its cycle structure, El. J. Combinat. 14 (2007) # R28 EXAMPLE Triangle starts at row n=1 1; 2; 3,1; 6,2,1; 12,7,4; 26,23,11,2; 59,71,41,8; 138,224,151,30; MAPLE Fx := proc(k) local ak ; ak := (2*x)^(2^k+1) ; (1-ak-(1-4*x+(ak*x*(2-ak))/(1-x))^(1/2))/(2*x-ak) ; end proc: ff := [] : for k from 0 to 5 do ff := [op(ff), taylor(Fx(k), x=0, 18)] ; end do : F := proc(n, k) global ff ; coeftayl(op(k+1, ff), x=0, n) ; end proc: T := proc(n, k) global ff ; if k = 0 then F(n, 0) ; else (F(n, k)-F(n, k-1))/2^k ; end if; end proc: for n from 1 to 17 do for k from 0 to 5 do if T(n, k) <> 0 then printf("%d, ", T(n, k)) ; fi; end do ; printf("\n") ; end do ; CROSSREFS Cf. A127384 (row sums). Sequence in context: A363266 A083855 A062565 * A156344 A218796 A119440 Adjacent sequences: A175134 A175135 A175136 * A175138 A175139 A175140 KEYWORD nonn,tabf AUTHOR R. J. Mathar, Feb 21 2010 STATUS approved

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Last modified September 17 23:36 EDT 2024. Contains 375991 sequences. (Running on oeis4.)