A213853 Rectangular array: (row n) = b**c, where b(h) = h, c(h) = binomial(2*n-4+2*h,n-2+h), n>=1, h>=1, and ** = convolution.

1, 4, 2, 13, 10, 6, 42, 38, 32, 20, 141, 136, 128, 110, 70, 492, 486, 476, 452, 392, 252, 1767, 1760, 1748, 1718, 1638, 1428, 924, 6474, 6466, 6452, 6416, 6316, 6036, 5280, 3432, 24051, 24042, 24026, 23984, 23864, 23514, 22506, 19734, 12870

Offset: 1

Author

Clark Kimberling, Jul 05 2012

Keywords

• nonn
• tabl
• easy

Comments

Row 1, (1,2,3,4,5,...)**(1,2,6,20,70,...):

Row 2, (1,2,3,4,5,...)**(2,6,20,70,252,...):

Row 3, (1,2,3,4,5,...)**(6,20,70,252,...):

For a guide to related arrays, see A213500.

Examples

			Northwest corner (the array is read by falling antidiagonals):
  1    4     13     42     141
  2    10    38     136    486
  6    32    128    476    1748
  20   110   452    1718   6416
  70   392   1638   6316   23864
		

Links

• Clark Kimberling, Antidiagonals n = 1..60, flattened

Crossrefs

Cf. A213500.

Programs

Mathematica

b[n_]:=n;c[n_]:=Binomial[2n-2,n-1]
t[n_,k_]:=Sum[b[k-i]c[n+i],{i,0,k-1}]
TableForm[Table[t[n,k],{n,1,10},{k,1,10}]]
Flatten[Table[t[n-k+1,k],{n,12},{k,n,1,-1}]]
r[n_]:=Table[t[n,k],{k,1,20}] (* A213853 *)