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A002553
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Coefficients for numerical differentiation.
(Formerly M5166 N2243)
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0
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1, 24, 640, 7168, 294912, 2883584, 54525952, 167772160, 36507222016, 326417514496, 5772436045824, 50577534877696, 1759218604441600, 15199648742375424, 261208778387488768, 2233785415175766016, 101457092405402533888
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) is the denominator of(-1)^(n-1)*Cn-1{1^2..(2n-1)^2}/((2n+1)!*2^(2n)), where Cn{1^2..(2n+1)^2} is equal to 1 when n=0, otherwise, it is the sum of the products of all possible combinations, of size n, of the numbers (2k+1)^2 with k=0,1,..,n. - Sean A. Irvine, after Ruperto Corso, Mar 29 2014
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MAPLE
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with(combinat): a:=n->add(mul(k, k=j), j=choose([seq((2*i-1)^2, i=1..n)], n))*(-1)^(n-1)/(2^(2*n)*(2*n+1)!):seq(a(n), n=0..20); # Sean A. Irvine, after Ruperto Corso
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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