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Search: id:A132950
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| A132950 |
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Generalization of an a(n)=3*2^n*a(n-1) as 3=(m+1) and 2=m To give general term: t(n,m)=a(n)=(m+1)^n*m^(n*(n-1)/2) ( here n taken first). |
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+0
1
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| 1, 1, 2, 1, 3, 18, 1, 4, 48, 1728, 1, 5, 100, 8000, 2560000, 1, 6, 180, 27000, 20250000, 75937500000, 1, 7, 294, 74088, 112021056, 1016255020032, 55316793250381824, 1, 8, 448, 175616, 481890304, 9256148959232, 1244544764462497792
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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From the ratio: a[2*n+1]/a[n]=(p/q)^(2*n)/(1/q)^(2*n+1)=q*p^(2*n) where p/q+1/q=1 or q=p+1 to give a[2*n+1]=(p+1)*p^(2*n)*a[2*n) Substitution of 2*n+1=m gives: a[m]=(p+1)*p^(m-1)*a[m] The general term is: a[n]=(p+1)^n*p(n*n-1)/2) Tha generalizes to the triangular sequence: t{n,m]=(m+1)^n*m^(n*(n-1)/2) There are a sequence of integer sequences. The row sums are: Table[If[m == 0, 1, (m + 1)^n*m^(n*(n - 1)/2)], {n, 0, m}]], {m, 0, 10}]; {1, 3, 22, 1781, 2568106, 75957777187, 55317809617497302, 1171356820508008315371465, 832644723581477539857134797829266, 22528399597273938808766298802728163594239911, 25937424603357947693143588829487172771562610524642332222}
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FORMULA
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If m==0,t(n,0)=1 else t(n,m)=a(n)=(m+1)^n*m^(n*(n-1)/2)
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EXAMPLE
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{1},
{1, 2},
{1, 3, 18},
{1, 4, 48, 1728},
{1, 5, 100, 8000, 2560000},
{1, 6, 180, 27000, 20250000, 75937500000},
{1, 7, 294, 74088, 112021056, 1016255020032, 55316793250381824}
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MATHEMATICA
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a = Table[Table[If[m == 0, 1, (m + 1)^n*m^(n*(n - 1)/2)], {n, 0, m}], {m, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A007447 A095852 A000618 this_sequence A106169 A014015 A108353
Adjacent sequences: A132947 A132948 A132949 this_sequence A132951 A132952 A132953
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 19 2007
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