OFFSET
1,2
LINKS
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
KEYWORD
nonn,tabf
AUTHOR
R. J. Mathar, Feb 21 2010
STATUS
approved