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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; text; internal format)
OFFSET
1,3
REFERENCES
S. G. Mikhlin, Constants in Some Inequalities of Analysis, Wiley, NY, 1986, see p. 59.
LINKS
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, 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.
Conjecture: +(n+1)*a(n) -2*n*a(n-1) -4*n*(n-1)^2*a(n-2)=0. - R. J. Mathar, Nov 24 2012
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:
MATHEMATICA
a[n_] := (n-1)! Binomial[n-1, Quotient[n-1, 2]];
Table[a[n], {n, 1, 19}] (* Jean-François Alcover, Apr 29 2023 *)
CROSSREFS
Cf. A059836.
Sequence in context: A156445 A304997 A060841 * A220266 A218917 A054759
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 25 2001
EXTENSIONS
More terms from James A. Sellers, Feb 26 2001 and from Larry Reeves (larryr(AT)acm.org), Feb 26 2001
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)