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Search: id:A064984
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| A064984 |
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Triangle of coefficients T[n,m] of polynomials n, n^2, (n+2n^3)/3, n^2(2+n^2)/3, n(3+10n^2+2n^4)/15, etc. after multiplication by the denominators (A049606). |
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1
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| 1, 0, 1, 1, 0, 2, 0, 2, 0, 1, 3, 0, 10, 0, 2, 0, 23, 0, 20, 0, 2, 45, 0, 196, 0, 70, 0, 4, 0, 132, 0, 154, 0, 28, 0, 1, 315, 0, 1636, 0, 798, 0, 84, 0, 2, 0, 5067, 0, 7180, 0, 1806, 0, 120, 0, 2, 14175, 0, 83754, 0, 50270, 0, 7392, 0, 330, 0, 4, 0, 146430, 0, 239327, 0, 74800, 0
(list; table; graph; listen)
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OFFSET
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1,6
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COMMENT
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These polynomials are P(1, n) = 2*Sum[k, {k,1,n-1}] + n, counting up to n and down again; P(2, m) = 2*Sum[P(1,n), {n,1,m-1}] + P(1,m), meaning up and down to n and this for n from 1 up to m and down again; etc.
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EXAMPLE
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1+2+3+2+1 = 3^2, (1)+(1+2+1)+(1+2+3+2+1)+(1+2+1)+(1) = (n+2n^3)/3.
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MATHEMATICA
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CoefficientList[ #, n ]&/@(NestList[ ((2*Sum[ #, {n, k-1} ]+(#/. n->k)//Simplify)/.k->n)&, n, -1+16 ] Denominator[ 2^#/#!&/@Range[ 16 ] ])
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CROSSREFS
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Row sums give A049606 again, final entry in each row seems to give A048896.
Sequence in context: A105166 A105783 A022879 this_sequence A038555 A138108 A158777
Adjacent sequences: A064981 A064982 A064983 this_sequence A064985 A064986 A064987
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KEYWORD
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nonn,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Oct 30 2001
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