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Search: id:A127878
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| A127878 |
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Numbers of the form x^4+4x^3+12x^2+24x+24. |
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+0
7
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| 24, 65, 168, 393, 824, 1569, 2760, 4553, 7128, 10689, 15464, 21705, 29688, 39713, 52104, 67209, 85400, 107073, 132648, 162569, 197304, 237345, 283208, 335433, 394584, 461249, 536040, 619593, 712568, 815649, 929544, 1054985, 1192728
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Generating polynomial is Schur's polynomial of 4-degree. Schur's polynomials n degree are n-th first term of series expansion of e^x function. All polynomials are non-reducible and belonging to the An alternating Galois transitive group if n is divisable by 4 or to Sn symmetric Galois Group in other case (proof Schur, 1930).
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FORMULA
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Integral representation in terms of incomplete Gamma function : a(n)= Exp[n]Gamma[5,n], where Gamma[5,n]= Integrate[x^4 Exp[ -x],{x,n,+infinity}]. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Jan 25 2008
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MATHEMATICA
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Table[24 + 24 x + 12 x^2 + 4 x^3 + x^4, {x, 0, 50}]
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CROSSREFS
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Cf. A127873, A127874, A127875, A127876, A127877, A127879, A127880, A127881, A127882, A127883, A127884.
Sequence in context: A022761 A090386 A118609 this_sequence A043154 A039331 A043934
Adjacent sequences: A127875 A127876 A127877 this_sequence A127879 A127880 A127881
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Feb 04 2007
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