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Search: id:A059837
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| 1, 1, 4, 18, 144, 1200, 14400, 176400, 2822400, 45722880, 914457600, 18441561600, 442597478400, 10685567692800, 299195895398400, 8414884558080000, 269276305858560000, 8646761377013760000, 311283409572495360000
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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S. G. Mikhlin, Constants in Some Inequalities of Analysis, Wiley, NY, 1986, see p. 59.
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FORMULA
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T(s, s) = (s-1)^2 * T(s-1, s-1) / floor(s/2) - Larry Reeves.
a(n)=sum{k=0..n, (-1)^(n+k)C(n, k)sum{i=0..n, C(n, floor(i/2))k^i} } - Paul Barry (pbarry(AT)wit.ie), Aug 05 2004
a(n)=(n-1)!*binomial(n-1,floor(n-1,2)), n>=1.
E.g.f. is the integral of the o.g.f. of A001405. With offset 0: e.g.f. is o.g.f. of A001405.
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MAPLE
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T := proc(s, t) option remember: if s=1 or t=1 then RETURN(1) fi: if t>1 and t mod 2 = 1 then RETURN(product((s-i)^2, i=1..(t-1)/2)) else RETURN((s-t/2)*product((s-i)^2, i=1..t/2-1)) fi: end: for s from 1 to 50 do printf(`%d, `, T(s, s)) od:
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CROSSREFS
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Cf. A059836.
Adjacent sequences: A059834 A059835 A059836 this_sequence A059838 A059839 A059840
Sequence in context: A034517 A065857 A060841 this_sequence A054759 A007153 A058924
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Feb 25 2001
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 26 2001, and from Larry Reeves (larryr(AT)acm.org), Feb 26 2001.
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