OFFSET
1,11
COMMENTS
Row sum sequence: Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, Length[CoefficientList[p[n, x], x]]}], {n, 0, 15}] {0, 1, 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835}
REFERENCES
G. J. Chaitin, Algorithmic Information Theory, Cambridge Univ. Press, 1987, page 169.
FORMULA
p(k, x) = Sum[p(j, x)*p(k - j, x), {j, 2, k - 1}].
EXAMPLE
Triangular sequence
{0},
{0, 1},
{1},
{0, 1},
{1, 0, 1},
{0, 3, 0, 1},
{2, 0, 6, 0, 1},
{0, 10, 0, 10, 0, 1},
{5, 0, 30, 0, 15, 0, 1},
{0, 35, 0, 70, 0, 21, 0, 1},
{14, 0, 140, 0, 140, 0, 28, 0, 1}
MAPLE
p := proc(k, x) option remember ; if k = 0 then 0 ; elif k= 1 then x; elif k= 2 then 1; else add(p(j, x)*p(k-j, x), j=2..k-1) ; fi ; end: A124027 := proc(n, k) coeftayl( p(n, x), x=0, k) ; end: printf("0, 0, 1, ") ; for n from 0 to 18 do for k from 0 to n-2 do printf("%d, ", A124027(n, k)) ; od: od: # R. J. Mathar, Oct 08 2007
MATHEMATICA
p[0, x] = 0; p[1, x] = x; p[2, x] = 1; p[k_, x_] := p[k, x] = Sum[p[j, x]*p[k - j, x], {j, 2, k - 1}]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Roger L. Bagula, Oct 31 2006
EXTENSIONS
Edited by N. J. A. Sloane, Oct 07 2007
More terms from R. J. Mathar, Oct 08 2007
STATUS
approved