A185875 Third accumulation array of A051340, by antidiagonals.

1, 4, 5, 10, 19, 15, 20, 46, 55, 35, 35, 90, 130, 125, 70, 56, 155, 250, 290, 245, 126, 84, 245, 425, 550, 560, 434, 210, 120, 364, 665, 925, 1050, 980, 714, 330, 165, 516, 980, 1435, 1750, 1820, 1596, 1110, 495, 220, 705, 1380, 2100, 2695, 3010, 2940, 2460, 1650, 715, 286, 935, 1875, 2940, 3920, 4606, 4830, 4500, 3630, 2365, 1001, 364, 1210, 2475, 3975, 5460, 6664, 7350, 7350, 6600, 5170

Offset: 1

Author

Clark Kimberling, Feb 05 2011

Keywords

• nonn
• tabl

Comments

A member of the accumulation chain A051340 < A141419 < A185874 < A185875 < A185876 < ... (See A144112 for the definition of accumulation array.)

Examples

			Northwest corner:
   1,   4,  10,  20,  35
   5,  19,  46,  90, 155
  15,  55, 130, 250, 425
  35, 125, 290, 550, 925
		

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.

Crossrefs

Cf. A051340, A141419, A144112, A185875, A185876.

Row 1: A000292; Column 1: A000332.

Programs

Mathematica

f[n_,k_]:= k*(1+k)*n*(1+n)*(2+n)*(5+4*k+3*n)/144;
TableForm[Table[f[n,k],{n,1,10},{k,1,15}]]
Table[f[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten

Formula

T(n,k) = (3*n+4*k+5)*C(k,2)*C(n,3)/12, k>=1, n>=1.