|
| |
|
|
A059837
|
|
Diagonal T(s,s) of triangle A059836.
|
|
2
| |
|
|
1, 1, 4, 18, 144, 1200, 14400, 176400, 2822400, 45722880, 914457600, 18441561600, 442597478400, 10685567692800, 299195895398400, 8414884558080000, 269276305858560000, 8646761377013760000, 311283409572495360000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
REFERENCES
| S. G. Mikhlin, Constants in Some Inequalities of Analysis, Wiley, NY, 1986, see p. 59.
|
|
|
FORMULA
| 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.
|
|
|
MAPLE
| 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:
|
|
|
CROSSREFS
| Cf. A059836.
Sequence in context: A065857 A156445 A060841 * A054759 A007153 A156870
Adjacent sequences: A059834 A059835 A059836 * A059838 A059839 A059840
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 25 2001
|
|
|
EXTENSIONS
| 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.
|
| |
|
|
