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).

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

Offset

1,1

Comments

Row n contains n+1 terms. Row sums yield the even-subscripted Lucas numbers (A005248).

Links

Table of n, a(n) for n=1..44.

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

Adjacent sequences: A104061 A104062 A104063 * A104065 A104066 A104067

Keyword

sign,tabf

Author

Emeric Deutsch, Mar 02 2005

Status

approved