A185731 Array by antidiagonals: T(n,k)=F*(k*n-n+3*k+13), where F = k*(k+1)*(k+2)*n*(n+1)*(n+2)/576.

1, 5, 4, 15, 21, 10, 35, 65, 55, 20, 70, 155, 175, 115, 35, 126, 315, 425, 375, 210, 56, 210, 574, 875, 925, 700, 350, 84, 330, 966, 1610, 1925, 1750, 1190, 546, 120, 495, 1530, 2730, 3570, 3675, 3010, 1890, 810, 165, 715, 2310, 4350, 6090, 6860, 6370, 4830, 2850, 1155, 220, 1001, 3355, 6600

Offset: 1

Author

Clark Kimberling, Feb 01 2011

Keywords

• nonn
• tabl

Comments

This is the accumulation array of A185730. (See A144112 for the definition of accumulation array.)

Examples

			Northwest corner:
1.....5....15....35....70
4.....21...65....155...315
10....55...175...425...875
20....115..375...925...1925
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A144112, A185730.

Programs

Mathematica

f[n_,k_]:=k(1+k)n(1+n)(7+2k-n+k*n)/36;
TableForm[Table[f[n,k],{n,1,10},{k,1,15}]]  (* A185730 *)
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}]; (* acc. arr. of {f(n,k)} *)
Factor[s[n,k]]  (* formula for A185731 *)
TableForm[Table[s[n,k],{n,1,10},{k,1,15}]] (* array A185731 *)
Table[s[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten (* A185731 *)

Formula

T(n,k) = F*(k*n-n+3*k+13), where F = k*(k+1)*(k+2)*n*(n+1)*(n+2)/576.