A189675 Composition of Catalan and Fibonacci numbers.

1, -1, 2, 2, -4, 3, -5, 10, -9, 5, 14, -28, 27, -20, 8, -42, 84, -84, 70, -40, 13, 132, -264, 270, -240, 160, -78, 21, -429, 858, -891, 825, -600, 351, -147, 34, 1430, -2860, 3003, -2860, 2200, -1430, 735, -272, 55, -4862, 9724, -10296, 10010, -8008, 5577, -3234, 1496, -495, 89, 16796, -33592, 35802, -35360, 29120, -21294, 13377, -7072, 2970, -890, 144, -58786, 117572, -125970, 125970, -106080, 80444, -53508, 30940, -15015, 5785, -1584, 233

Offset: 1

Author

Wouter Meeussen, Apr 25 2011

Keywords

• sign
• tabl

Comments

Row sums equal 1 (proof by Bill Gosper, Apr 17 2011). Row sums of absolute terms equal A081696.

Examples

			Table starts
   1,
  -1,  2,
   2, -4,  3,
  -5, 10, -9, 5,
		

References

• Email of R. W. Gosper on the math-fun mailing list, Apr 17 2011.

Crossrefs

Cf. A081696, A171567, A064310.

Programs

Mathematica

Table[(-1)^(k + n) k/(2n - k) Binomial[2n - k, n - k] Fibonacci[k + 1], {n, 12}, {k, n}]