# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a366149 Showing 1-1 of 1 %I A366149 #10 Jan 05 2024 13:46:32 %S A366149 1,1,1,1,8,8,1,26,190,190,1,60,1270,9080,9080,1,115,5180,102320, %T A366149 725320,725320,1,196,15960,644960,12334600,87067520,87067520,1,308, %U A366149 40908,2894900,110761200,2080769120,14652451360,14652451360 %N 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. %C A366149 This a weighted generalized Catalan triangle (A365673) with the heptagonal numbers as weights. %e A366149 Triangle T(n, k) starts: %e A366149 [0] 1; %e A366149 [1] 1, 1; %e A366149 [2] 1, 8, 8; %e A366149 [3] 1, 26, 190, 190; %e A366149 [4] 1, 60, 1270, 9080, 9080; %e A366149 [5] 1, 115, 5180, 102320, 725320, 725320; %e A366149 [6] 1, 196, 15960, 644960, 12334600, 87067520, 87067520; %e A366149 [7] 1, 308, 40908, 2894900, 110761200, 2080769120, 14652451360, 14652451360; %p A366149 T := proc(n, k) option remember; %p A366149 if k = 0 then 1 else if k = n then T(n, k-1) else %p A366149 (((5*k - 5*n - 2)*(k - n - 1))/2) * T(n, k - 1) + T(n - 1, k) fi fi end: %p A366149 seq(seq(T(n, k), k = 0..n), n = 0..8); %t A366149 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]]; %t A366149 Table[A366149[n, k], {n,0,10}, {k,0,n}] (* _Paolo Xausa_, Jan 01 2024 *) %Y A366149 Cf. A000566, A366150 (main diagonal), A365673 (general case). %K A366149 nonn,tabl %O A366149 0,5 %A A366149 _Peter Luschny_, Oct 01 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE