A260630 Numerators of first derivatives of Catalan numbers (as continuous functions of n).
-1, 1, 5, 59, 449, 1417, 16127, 429697, 437705, 7549093, 145103527, 146489197, 3396112211, 2442184933, 7369048679, 429556076057, 13374954901367, 13427048535167, 94315062045929, 3500487562166393, 3510273150915593, 144285489968702713, 6218562602767668259
Offset: 0
Examples
For n = 3, C'(3) = 59/12, so a(3) = numerator(59/12) = 59.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
Numerator@FunctionExpand@Table[CatalanNumber'[n] , {n, 0, 22}]
Formula
a(n) = numerator(d(n)), where d(n) satisfies recurrence: d(0) = -1, d(1) = 1/2, (n+1)^2*d(n) = 2*(4*n^2-2*n-1)*d(n-1) - 4*(2*n-3)^2*d(n-2).
Comments