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A140982 If (a_n) is a sequence then let L(a_n)=(b_n) where b_n = a_n^2 - a_{n-1} a_{n+1}. The given sequence is the rows of the triangle obtained by computing L^2(binomial(n,k)). 0
1, 3, 1, 6, 16, 1, 10, 100, 50, 1, 15, 400, 750, 120, 1, 21, 1225, 6125, 3675, 245, 1, 28, 3136, 34300, 54880, 13720, 448, 1, 36, 7056, 148176, 518616, 345744, 42336, 756, 1, 45, 14400, 529200, 3556224, 5186160, 1693440, 113400, 1200, 1, 55, 27225, 1633500 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
3,2
COMMENTS
L(binomial(n,k)) gives the Narayana numbers, A001263.
LINKS
Peter R. W. McNamara and Bruce E. Sagan, Infinite log-concavity: developments and conjectures, arXiv:0808.1065 [math.CO], 2008-2009.
Peter R. W. McNamara and Bruce E. Sagan, Infinite log-concavity: developments and conjectures, Advances in Applied Mathematics, 44 (1) (2010), 1-15.
FORMULA
a(n,k) = binomial(n,k)^2 * binomial(n,k-1) * binomial(n,k-2) / (n*binomial(n,2)).
MATHEMATICA
a[n_, k_] := 2 * Binomial[n, k]^2 * Binomial[n, k - 1] * Binomial[n, k - 2] / ((n - 1) n^2); Table[ a[n, k], {n, 2, 11}, {k, 2, n}] // Flatten (* Robert G. Wilson v, Aug 03 2008 *)
CROSSREFS
Cf. A001263.
Sequence in context: A049966 A187120 A350610 * A100232 A221937 A333652
KEYWORD
nonn,tabl
AUTHOR
Bruce E. Sagan, Jul 28 2008
EXTENSIONS
More terms from Robert G. Wilson v, Aug 03 2008
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)