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 A157322 Symmetrical Hahn weights on q-form factorials:m=3;q=4; 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])]. 0
 1, 7560, 7560, 49920, 198450, 49920, 214200, 1965600, 1965600, 214200, 696384, 11245500, 25958400, 11245500, 696384, 1871016, 45700200, 185640000, 185640000, 45700200, 1871016, 4377600, 147342510, 905299200, 1593112500, 905299200 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are: {1, 15120, 298290, 4359600, 49842168, 466422432, 3707151120, 25761076800, 160081662720, 905384837376, 4726028289024,...}. These are Rhombi sides as ratios of q-form to factorial: r1=t(1,n)/n!; r2=t(m+1,k]/(n-k)!; r3=t(m+1,n-k)/(n-k)! They get very large very fast, but all are integer. LINKS FORMULA m=3;q=4; 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])]. EXAMPLE {1}, {7560, 7560}, {49920, 198450, 49920}, {214200, 1965600, 1965600, 214200}, {696384, 11245500, 25958400, 11245500, 696384}, {1871016, 45700200, 185640000, 185640000, 45700200, 1871016}, {4377600, 147342510, 905299200, 1593112500, 905299200, 147342510, 4377600}, {9224280, 402192000, 3405249120, 9063873000, 9063873000, 3405249120, 402192000, 9224280}, {17908800, 968549400, 10622976000, 38963908200, 58934977920, 38963908200, 10622976000, 968549400, 17908800}, {32556744, 2115477000, 28779753600, 136745280000, 285019351344, 285019351344, 136745280000, 28779753600, 2115477000, 32556744}, {56077056, 4273072650, 69844320000, 411633495000, 1111428864000, 1531556631612, 1111428864000, 411633495000, 69844320000, 4273072650, 56077056} MATHEMATICA Clear[t, n, m, i, k, a, b]; t[n_, m_] = If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b[n_, k_, m_] = If[n == 0, 1, (n!*t[m + 1, k]*t[m + 1, n - k])/(k!*(n - k)!*t[ 1, n])]; Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}] CROSSREFS Sequence in context: A077096 A031137 A210171 * A172443 A190108 A145313 Adjacent sequences:  A157319 A157320 A157321 * A157323 A157324 A157325 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 26 2009 STATUS approved

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