OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
T(n,k) = C(k+3,4)*C(n+2,3)*(k*n-n+3*k+17)/20, k>=1, n>=1.
T(n,k) = Sum_{j=1..n} Sum_{l=1..k} A185733(j,l), by definition.
EXAMPLE
Northwest corner:
1....6......21.....56....126
4....25.....90....245....560
10...65....240....665...1540
20...135...510...1435...3360
MATHEMATICA
f[n_, k_]:= k*(1+k)*(2+k)*n*(1+n)*(10+2*k-n+k*n)/144;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* array A185733 *)
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten (* A185733 *)
s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* accumulation array of {f(n, k)} *)
FullSimplify[s[n, k]] (* the formula for A185734 *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* array A185734 *)
Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten (* A185734 *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Feb 02 2011
STATUS
approved