A366149 Triangle read by rows. T(n, k) = A000566(n - k + 1) * T(n, k - 1) + T(n - 1, k) for 0 < k < n. T(n, 0) = 1 and T(n, n) = T(n, n - 1) if n > 0.

1, 1, 1, 1, 8, 8, 1, 26, 190, 190, 1, 60, 1270, 9080, 9080, 1, 115, 5180, 102320, 725320, 725320, 1, 196, 15960, 644960, 12334600, 87067520, 87067520, 1, 308, 40908, 2894900, 110761200, 2080769120, 14652451360, 14652451360

Offset: 0

Author

Peter Luschny, Oct 01 2023

Keywords

• nonn
• tabl

Comments

This a weighted generalized Catalan triangle (A365673) with the heptagonal numbers as weights.

Examples

			Triangle T(n, k) starts:
[0] 1;
[1] 1,   1;
[2] 1,   8,     8;
[3] 1,  26,   190,     190;
[4] 1,  60,  1270,    9080,      9080;
[5] 1, 115,  5180,  102320,    725320,     725320;
[6] 1, 196, 15960,  644960,  12334600,   87067520,    87067520;
[7] 1, 308, 40908, 2894900, 110761200, 2080769120, 14652451360, 14652451360;
		

Crossrefs

Cf. A000566, A366150 (main diagonal), A365673 (general case).

Programs

Maple

T := proc(n, k) option remember;
if k = 0 then 1 else if k = n then T(n, k-1) else
(((5*k - 5*n - 2)*(k - n - 1))/2) * T(n, k - 1) + T(n - 1, k) fi fi end:
seq(seq(T(n, k), k = 0..n), n = 0..8);

Mathematica

A366149[n_, k_] := A366149[n, k] = Which[k==0, 1, k==n, A366149[n, k-1], True, PolygonalNumber[7, n-k+1] A366149[n, k-1] + A366149[n-1, k]];
Table[A366149[n, k], {n,0,10}, {k,0,n}] (* Paolo Xausa, Jan 01 2024 *)