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Search: id:A143165
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| A143165 |
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Sequence from the exponential generating function arcsin(2*x)/(2*(1-2*x)^(3/2)). |
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+0
2
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| 0, 1, 6, 49, 468, 5469, 73362, 1138005, 19737000, 383284665, 8163588510, 190709475705, 4818820261500, 131650382056725, 3850053335966250, 120466494638624925, 4002649276431128400, 141156781966460192625, 5252646220794868029750, 206149276075766825426625
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OFFSET
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0,3
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COMMENT
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Used in A024199(n+1)= A003148(n) + a(n).
Binomial convolution of [0,1^2,0,2^2,0,...,0,((2*k)!/k!)^2,0,...] (e.g.f. arcsin(2*x)/2) with the double factorials A001147.
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FORMULA
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E.g.f.: arcsin(2*x)/(2*(1-2*x)^(3/2)).
a(n)=sum(binomial(n,2*k+1)*(4^k)*((2*k-1)!!)^2*(2*(n-2*k)-1)!!,k=0..floor(n/2)), with (2*n-1)!!:= A001147(n) (double factorials).
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EXAMPLE
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a(3) + A003148(3) = 49 + 27 = 76 = A024199(4).
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CROSSREFS
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Sequence in context: A104170 A098306 A055847 this_sequence A008786 A046195 A024268
Adjacent sequences: A143162 A143163 A143164 this_sequence A143166 A143167 A143168
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 15 2008
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