OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Johann Cigler, Some elementary observations on Narayana polynomials and related topics, arXiv:1611.05252 [math.CO], 2016. See p. 24.
FORMULA
T(n,k) = (4*n+5*k+11)*C(k+2,3)*C(n+4,4)/20, k>=1, n>=1.
EXAMPLE
Northwest corner:
1, 5, 15, 35, 70
6, 29, 85, 195, 385
21, 99, 285, 645, 1260
56, 259, 735, 1645, 3185
MATHEMATICA
f[n_, k_]:=k(1+k)n(1+n)(2+n)(5+4k+3n)/144;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185875 *)
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* accumulation array of {f(n, k)} *)
Factor[s[n, k]] (* formula for A185876 *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185876 *)
Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 05 2011
STATUS
approved