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A104064 Triangle read by rows: T(n,k)=(-1)^k*(2n/(2n-k))5^(n-k)*binomial(2n-k,k) (0<=k<=n, n>=1). 0
5, -2, 25, -20, 2, 125, -150, 45, -2, 625, -1000, 500, -80, 2, 3125, -6250, 4375, -1250, 125, -2, 15625, -37500, 33750, -14000, 2625, -180, 2, 78125, -218750, 240625, -131250, 36750, -4900, 245, -2, 390625, -1250000, 1625000, -1100000, 412500, -84000, 8400, -320, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row n contains n+1 terms. Row sums yield the even-subscripted Lucas numbers (A005248).
LINKS
P. Filipponi, Waring's formula, the binomial formula and generalized Fibonacci matrices, The Fibonacci Quarterly, 30, 1992, 225-231.
P. Filipponi, Combinatorial expressions for Lucas numbers, The Fibonacci Quarterly, 36, 1998, 63-65.
EXAMPLE
Triangle starts:
5, -2;
25, -20, 2;
125, -150, 45, -2;
625, -1000, 500, -80, 2; - Michel Marcus, Apr 09 2013
MAPLE
T:=proc(n, k) if k<=n then (-1)^k*2*n*5^(n-k)*binomial(2*n-k, k)/(2*n-k) else 0 fi end: for n from 1 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
CROSSREFS
Cf. A005248.
Sequence in context: A090882 A191702 A164309 * A038244 A135138 A128712
KEYWORD
sign,tabf
AUTHOR
Emeric Deutsch, Mar 02 2005
STATUS
approved

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Last modified March 4 12:21 EST 2024. Contains 370532 sequences. (Running on oeis4.)