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A156645 A q combination based on Shabat ChebyshevT (*A123583*) Polynomials:m=1;q=2; 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, 36, 1, 1, 1225, 1225, 1, 1, 41616, 1416100, 41616, 1, 1, 1413721, 1634261476, 1634261476, 1413721, 1, 1, 48024900, 1885939157025, 64069586905104, 1885939157025, 48024900, 1, 1, 1631432881, 2176372249076025 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 18, 452, 50374, 17210316, 26473387956, 125754936641832,

2692503748294554438, 178119744099983099364620, 53115099293451187427426853340,...}.

LINKS

Table of n, a(n) for n=0..30.

FORMULA

m=1;q=2;

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, 16, 1},

{1, 225, 225, 1},

{1, 3136, 44100, 3136, 1},

{1, 43681, 8561476, 8561476, 43681, 1},

{1, 608400, 1660970025, 23150231104, 1660970025, 608400, 1},

{1, 8473921, 322220846025, 62555239000969, 62555239000969, 322220846025, 8473921, 1},

{1, 118026496, 62509200188176, 169024877308827904, 2354328975040469284, 169024877308827904, 62509200188176, 118026496, 1},

{1, 1643897025, 12126462852848400, 456705280997653184784, 88603154642529399752100, 88603154642529399752100, 456705280997653184784, 12126462852848400, 1643897025, 1},

{1, 22896531856, 2352471287556008025, 1234017524492640137505024, 3334492032897384440894996964, 46443647187902490644456769600, 3334492032897384440894996964, 1234017524492640137505024, 2352471287556008025, 22896531856, 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: A181635 A174673 A203277 * A330084 A037935 A159824

Adjacent sequences:  A156642 A156643 A156644 * A156646 A156647 A156648

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 12 2009

STATUS

approved

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Last modified January 22 11:21 EST 2021. Contains 340362 sequences. (Running on oeis4.)