0,9

Zig-Zag numbers (see the Conway and Guy reference p. 110 and the J.-P. Delahaye reference, p. 31).

Approximation to Pi: 2*n*a(n-1,n-1)/a(n,n), n>=3. See A132049(n)/A132050(n). See the Delahaye reference, p. 31.

Arnold, V. I., Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics, Duke Math. J. 63 (1991), 537-555.

V. I. Arnold, The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups, Uspekhi Mat. nauk., 47 (#1, 1992), 3-45 = Russian Math. Surveys, Vol. 47 (1992), 1-51.

J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, p. 110.

J.-P. Delahaye, Pi - die Story (German translation), Birkhaeuser, 1999 Basel, p. 31. French original: Le fascinant nombre Pi, Pour la Science, Paris, 1997.

C. Poupard, De nouvelles significations enumeratives des nombres d'Entringer, Discrete Math., 38 (1982), 265-271.

B. Gourevitch, L'univers de Pi

J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon on transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).

a(0,0)=1, a(n,m)=0 if n<m, a(n,m)=0 if m<0 else sum(a(n-1,n-k),k=1..m).

This version of the triangle begins:

.............1

...........0...1

.........0...1...1

.......0...1...2...2

.....0...2...4...5...5

...0...5..10..14..16..16

See A008280 and A108040 for other versions.

A008281 := proc(h, k) option remember ; if h=1 and k=1 or h=0 then RETURN(1) ; elif h>=1 and k> h then RETURN(0) ; elif h=k then RETURN( A008281(h, h-1)) ; else RETURN( add(A008281(h-1, j), j=h-k..h-1) ) ; fi ; end: for h from 0 to 10 do for k from 0 to h do printf("%d, ", A008281(h, k)) ; od ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 27 2006

Cf. A008280.

Sequence in context: A159916 A159286 A006462 this_sequence A094671 A021458 A099064

Adjacent sequences: A008278 A008279 A008280 this_sequence A008282 A008283 A008284

nonn,tabl,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).