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

1,2

Comments

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

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.

Formula

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

Example

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

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

Crossrefs

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

Row 1: A000292; Column 1: A000332.

Sequence in context: A049897 A049867 A054173 * A354080 A049898 A166577

Adjacent sequences: A185872 A185873 A185874 * A185876 A185877 A185878

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 05 2011

Status

approved