# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a157320 Showing 1-1 of 1 %I A157320 #2 Mar 30 2012 17:34:34 %S A157320 1,6,6,8,18,8,10,36,36,10,12,60,96,60,12,14,90,200,200,90,14,16,126, %T A157320 360,500,360,126,16,18,168,588,1050,1050,588,168,18,20,216,896,1960, %U A157320 2520,1960,896,216,20,22,270,1296,3360,5292,5292,3360,1296,270,22,24,330 %N A157320 Symmetrical Hahn weights on q-form factorials:m=1;q=2; q-form:t(n,m)=If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; Hahn weight:b(n,k,m)=If[n == 0, 1, (n!*t[m + 1, k]*t[m + 1, n - k])/(k!*(n - k)!*t[1, n])]. %C A157320 Row sums are: %C A157320 {1, 12, 34, 92, 240, 608, 1504, 3648, 8704, 20480, 47616,...}. %C A157320 These are Rhombi sides as ratios of q-form to factorial: %C A157320 r1=t(1,n)/n!; %C A157320 r2=t(m+1,k]/(n-k)!; %C A157320 r3=t(m+1,n-k)/(n-k)! %C A157320 They get very large very fast, but all are integer. %F A157320 m=1;q=2; %F A157320 q-form:t(n,m)=If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; %F A157320 Hahn weight: %F A157320 b(n,k,m)=If[n == 0, 1, (n!*t[m + 1, k]*t[m + 1, n - k])/(k!*(n - k)!*t[1, n])]. %e A157320 {1}, %e A157320 {6, 6}, %e A157320 {8, 18, 8}, %e A157320 {10, 36, 36, 10}, %e A157320 {12, 60, 96, 60, 12}, %e A157320 {14, 90, 200, 200, 90, 14}, %e A157320 {16, 126, 360, 500, 360, 126, 16}, %e A157320 {18, 168, 588, 1050, 1050, 588, 168, 18}, %e A157320 {20, 216, 896, 1960, 2520, 1960, 896, 216, 20}, %e A157320 {22, 270, 1296, 3360, 5292, 5292, 3360, 1296, 270, 22}, %e A157320 {24, 330, 1800, 5400, 10080, 12348, 10080, 5400, 1800, 330, 24} %t A157320 Clear[t, n, m, i, k, a, b]; %t A157320 t[n_, m_] = If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; %t A157320 b[n_, k_, m_] = If[n == 0, 1, (n!*t[m + 1, k]*t[m + 1, n - k])/(k!*(n - k)!*t[ 1, n])]; %t A157320 Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}] %K A157320 nonn,tabf,uned %O A157320 0,2 %A A157320 _Roger L. Bagula_, Feb 26 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE