OFFSET
0,2
COMMENTS
Row sums are A097472(n).
FORMULA
T(n,k) = A037027(n+k+1, 2*k+1).
T(n,k) = T(n-1,k-1) + 2*T(n-1,k) + T(n-2,k) - 2*T(n-3,k) - T(n-4,k), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n.
G.f.: -1/(x*y-x^4-2*x^3+x^2+2*x-1). - Vladimir Kruchinin, Apr 29 2015
EXAMPLE
Triangle begins:
1;
2, 1;
5, 4, 1;
10, 14, 6, 1;
20, 40, 27, 8, 1;
38, 105, 98, 44, 10, 1;
71, 256, 315, 192, 65, 12, 1;
130, 594, 924, 726, 330, 90, 14, 1;
...
MATHEMATICA
T[0, 0] = 1; T[n_, k_] := SeriesCoefficient[-1/(x*y - x^4 - 2*x^3 + x^2 + 2*x - 1), {x, 0, n}, {y, 0, k}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 29 2015, after Vladimir Kruchinin *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Feb 20 2014
STATUS
approved