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 A156646 A q combination based on Shabat ChebyshevT (*A123583*) Polynomials:m=10;q=11; t(n,k)=If[m == 0, n!, Product[1 - ChebyshevT[k, m + 1]^2, {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, 484, 1, 1, 233289, 233289, 1, 1, 112444816, 54198633636, 112444816, 1, 1, 54198168025, 12591535188240100, 12591535188240100, 54198168025, 1, 1, 26123404543236, 2925290638056514680225, 1409984043580226203632400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 486, 466580, 54423523270, 25183178772816252, 1415834624908586042079324, 315777781711456436216361525791592, 8557141455015333552622338466625683918929990, 919904875455988058805918203281265383284735257679581420, 12015316940284582094553740757509771935923449985321087298560435616756,...}. All the Shabat levels between m=1 and m=15 are Integers, but the ChebvyshevT q-combinations are rational. LINKS FORMULA m=10;q=11; t(n,k)=If[m == 0, n!, Product[1 - ChebyshevT[k, m + 1]^2, {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, 484, 1}, {1, 233289, 233289, 1}, {1, 112444816, 54198633636, 112444816, 1}, {1, 54198168025, 12591535188240100, 12591535188240100, 54198168025, 1}, {1, 26123404543236, 2925290638056514680225, 1409984043580226203632400, 2925290638056514680225, 26123404543236, 1}, {1, 12591426791671729, 679609371602026315384502841, 157888211246356603490438586721225, 157888211246356603490438586721225, 679609371602026315384502841, 12591426791671729, 1}, {1, 6069041590181230144, 157888208426400692187663709602064, 17680120114234397423891350742345674486336, 8521781214471088340921742242682484788292900, 17680120114234397423891350742345674486336, 157888208426400692187663709602064, 6069041590181230144, 1}, {1, 2925265455040561257681, 36680904357358652250958517345785844496, 1979797255198461989855654149382312098871621344656, 459950457930738794260064888627828133106296370871343876, 459950457930738794260064888627828133106296370871343876, 1979797255198461989855654149382312098871621344656, 36680904357358652250958517345785844496, 2925265455040561257681, 1}, {1, 1409971880287960344972100, 8521781061952388599826634530660791324082025, 221695166456231612382854811257286078980114818629412814400, 24825141414265983818472195501503270798474206263930637396729676100, 11965666657012659794004316098178931867034726941620174489004812527504, 24825141414265983818472195501503270798474206263930637396729676100, 221695166456231612382854811257286078980114818629412814400, 8521781061952388599826634530660791324082025, 1409971880287960344972100, 1} MATHEMATICA Clear[t, n, m, i, k, a, b]; t[n_, m_] = If[m == 0, n!, Product[1 - ChebyshevT[k, m + 1]^2, {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: A158330 A288082 A251625 * A177434 A202444 A329872 Adjacent sequences:  A156643 A156644 A156645 * A156647 A156648 A156649 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 12 2009 STATUS approved

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Last modified January 22 10:40 EST 2021. Contains 340362 sequences. (Running on oeis4.)