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Search: id:A126936
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| A126936 |
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Coefficients of a polynomial representation of the integral of 1/(x^4+2ax^2+1)^(n+1) from x= 0 to infinity. |
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+0
1
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| 0, 4, 4, 36, 60, 24, 288, 688, 560, 160, 2240, 7080, 8760, 5040, 1120, 17304, 68712, 114576, 99456, 44352, 8064, 133672, 642824, 1351840, 1572480, 1055040, 384384, 59136, 1034880, 5864640, 14912064, 21778560, 19536000, 10695168, 3294720
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The integral N(a;n)=int(x=0..infinity) 1/(x^4+2*a*x^2+1)^(n+1) has a polynomial representation P_n(a)= 2^(n+3/2)*(a+1)^(n+1/2)*N(a;n)/pi The table contains the coefficients T(l,n) of P_n(a)=2^(-2*n)* sum(l=0..n) T(l,n)*a^l in row n and column 0<=l<=n.
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LINKS
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V. H. Moll, Combinatorial sequences arising from a rational intgral, Onl. J. Anal. Combin. no 2 (2007) #4.
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EXAMPLE
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The table starts
0
4,4
36,60,24
288,688,560,160
2240,7080,8760,5040,1120
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MAPLE
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T := proc(l, m) add(2^k*binomial(2*m-2*k, m-k)*binomial(m+k, m)*binomial(k, l), k=1..m); end: for m from 0 to 11 do for l from 0 to m do printf("%d, ", T(l, m)); od; od;
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CROSSREFS
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Adjacent sequences: A126933 A126934 A126935 this_sequence A126937 A126938 A126939
Sequence in context: A001443 A089542 A105350 this_sequence A129357 A100303 A111882
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2007
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