A174297 First column of A174295.

1, -1, -1, 0, -1, 1, -3, 6, -15, 36, -91, 232, -603, 1585, -4213, 11298, -30537, 83097, -227475, 625992, -1730787, 4805595, -13393689, 37458330, -105089229, 295673994, -834086421, 2358641376, -6684761125, 18985057351, -54022715451

Offset

0,7

Comments

First 6 terms as in Mobius function A008683. Signed version of A099323 with an additional leading 1.

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

Cf. 099323, A112467, A112468, A174294, A174295, A174296.

Sequence in context: A017924 A052827 A033192 * A005043 A099323 A342912

Adjacent sequences: A174294 A174295 A174296 * A174298 A174299 A174300

Keyword

sign

Author

Mats Granvik, Mar 15 2010

Status

approved