OFFSET
0,7
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = -(-3)^(n-3/2)*hypergeometric2F1([3/2, n-1],[2],4) for n > 2. - Mark van Hoeij, Jul 02 2010
a(n) = (-1)^n if n < 2 otherwise Sum_{j=0..n-2} (-1)^(j-1)*binomial(n-2, j)*Catalan(j). - G. C. Greubel, Nov 25 2021
MATHEMATICA
a[n_]:= a[n]= If[n<2, (-1)^n, Sum[(-1)^(j+1)*Binomial[n-2, j]*CatalanNumber[j], {j, 0, n-2}]]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, Nov 25 2021 *)
PROG
(Magma)
a:= func< n | n lt 2 select (-1)^n else (&+[(-1)^(k+1)*Binomial(n-2, k)*Catalan(k): k in [0..n-2]]) >;
[a(n): n in [0..30]]; // G. C. Greubel, Nov 25 2021
(Sage) [1, -1]+[sum( (-1)^(j+1)*binomial(n-2, j)*catalan_number(j) for j in (0..n-2) ) for n in (2..40)] # G. C. Greubel, Nov 25 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Mats Granvik, Mar 15 2010
STATUS
approved