This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
This version of the triangle begins: .............1 ...........1...0 .........0...1...1 .......2...2...1...0 .....0...2...4...5...5 ..16..16..14..10...5...0 Kempner tableau begins: ....................1 ....................1....0 ...............0....1....1 ...............2....2....1....0 ..........0....2....4....5....5 .........16...16...14...10....5...0 .....0...16...32...46...56...61..61 ...272..272..256..224..178..122..61..0 Column 1,1,1,2,4,14,46,224, ... is A005437. Column 1,1,5,10,56,178, ... is A005438.
a108040 n k = a108040_tabl !! n !! k a108040_row n = a108040_tabl !! k a108040_tabl = ox False a008281_tabl where ox turn (xs:xss) = (if turn then reverse xs else xs) : ox (not turn) xss -- Reinhard Zumkeller, Nov 01 2013
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: A008280 := proc(h,k) if ( h <= 1 ) or ( h mod 2) = 1 then A008281(h,k) ; else A008281(h,h-k) ; fi ; end: A108040 := proc(h,k) A008280(h,h-k) ; end: for h from 0 to 13 do for k from 0 to h do printf("%d, ",A108040(h,k)) ; od ; od ; # R. J. Mathar, May 02 2007
max = 11; t[0, 0] = 1; t[n_, m_] /; nA008280 = {Reverse[#[[1]]], #[[2]]}& /@ Partition[tri, 2] // Flatten[#, 1]&; A108040 = Reverse /@ A008280; A108040 // Flatten (* Jean-François Alcover, Jan 08 2014 *) T[0,0]:=1; T[n_?OddQ,k_]/;0<=k<=n := T[n,k]=T[n,k+1]+T[n-1,k]; T[n_?EvenQ,k_]/;0<=k<=n := T[n,k]=T[n,k-1]+T[n-1,k-1]; T[n_,k_] := 0; Flatten@Table[T[n,k], {n,0,10}, {k,0,n}] (* Oliver Seipel, Nov 24 2024 *)
# Uses function seidel from A008281. def A108040row(n): return seidel(n)[::-1] if n % 2 else seidel(n) for n in range(8): print(A108040row(n)) # Peter Luschny, Jun 01 2022
1;
1, 1;
2, 1, 2;
5, 2, 5, 4;
16, 5, 16, 10, 14;
61, 16, 61, 32, 56, 46;
272, 61, 272, 122, 256, 178, 224;
1385, 272, 1385, 544, 1324, 800, 1202, 1024;
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