OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
T(n,k) = C(k+1,2)*C(n+1,2)*(n^2+3*n+2*k)/6, k>=1, n>=1.
EXAMPLE
Northwest corner:
1.....4.....10.....20.....35
6.....21....48.....90.....150
20....66....144....260....420
50....160...340....600....950
MATHEMATICA
f[n_, k_]:=(k*n/6)(-2+3k+3n+2n^2);
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* array A185912 *)
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}];
FullSimplify[s[n, k]] (* formula for A185913 *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* array A185913 *)
Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 06 2011
STATUS
approved