login
A360313
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n-1-k,n-2*k) * binomial(2*k,k).
3
1, 0, -2, -2, 4, 10, -4, -38, -22, 114, 188, -234, -914, -18, 3376, 3338, -9416, -21718, 14416, 96338, 39274, -328558, -471344, 795398, 2586064, -517690, -10453424, -8272658, 32186818, 63596494, -61876584, -307070174, -62655330, 1129250706, 1356328788
OFFSET
0,3
LINKS
FORMULA
G.f.: 1 / sqrt(1+4*x^2/(1-x)).
n*a(n) = 2*(n-1)*a(n-1) - (5*n-6)*a(n-2) + 2*(2*n-5)*a(n-3).
MATHEMATICA
RecurrenceTable[{a[0]==1, a[1]==0, a[2]==-2, a[n]==1/n (2(n-1)a[n-1]-(5n-6)a[n-2]+2(2n-5)a[n-3])}, a, {n, 40}] (* Harvey P. Dale, Sep 20 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n-1-k, n-2*k)*binomial(2*k, k));
(PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1+4*x^2/(1-x)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 03 2023
STATUS
approved