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 A158117 Triangle sequence of general q-combinations: m=3; t(n,m)=t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]. 0
 1, 1, 1, 1, 10, 1, 1, 100, 100, 1, 1, 1000, 10000, 1000, 1, 1, 10000, 1000000, 1000000, 10000, 1, 1, 100000, 100000000, 1000000000, 100000000, 100000, 1, 1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 12, 202, 12002, 2020002, 1200200002, 2020002000002, 12002000020000002, 202000200000200000002, 12002000020000002000000002,...}. LINKS FORMULA m=3; t(n,m)=t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]. EXAMPLE {1}, {1, 1}, {1, 10, 1}, {1, 100, 100, 1}, {1, 1000, 10000, 1000, 1}, {1, 10000, 1000000, 1000000, 10000, 1}, {1, 100000, 100000000, 1000000000, 100000000, 100000, 1}, {1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1}, {1, 10000000, 1000000000000, 1000000000000000, 10000000000000000, 1000000000000000, 1000000000000, 10000000, 1}, {1, 100000000, 100000000000000, 1000000000000000000, 100000000000000000000, 100000000000000000000, 1000000000000000000, 100000000000000, 100000000, 1}, {1, 1000000000, 10000000000000000, 1000000000000000000000, 1000000000000000000000000, 10000000000000000000000000, 1000000000000000000000000, 1000000000000000000000, 10000000000000000, 1000000000, 1} MATHEMATICA t[n_, m_] = If[m == 0, n!, Product[((m + 1)*((m + 1) + 1)/2)^k, {k, 1, n}]]; b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]; Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}] CROSSREFS Sequence in context: A160562 A176243 A022173 * A172378 A015124 A156767 Adjacent sequences:  A158114 A158115 A158116 * A158118 A158119 A158120 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 12 2009 STATUS approved

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Last modified September 29 06:29 EDT 2020. Contains 337425 sequences. (Running on oeis4.)