A360211 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-3*k,n-2*k).
1, 2, 5, 17, 61, 221, 812, 3021, 11344, 42899, 163146, 623320, 2390653, 9198879, 35494701, 137290466, 532149805, 2066501909, 8038146035, 31312535610, 122140123201, 477002869614, 1864912495716, 7298427590543, 28588888586743, 112080607196843, 439744801379594
Offset: 0
Keywords
Programs
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Maple
A360211 := proc(n) add((-1)^k*binomial(2*n-3*k,n-2*k),k=0..floor(n/2)) ; end proc: seq(A360211(n),n=0..40) ; # R. J. Mathar, Mar 02 2023
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PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n-3*k, n-2*k));
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PARI
my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1+2*x^2/(1+sqrt(1-4*x)))))
Formula
G.f.: 1 / ( sqrt(1-4*x) * (1 + x^2 * c(x)) ), where c(x) is the g.f. of A000108.
a(n) ~ 2^(2*n+3) / (9*sqrt(Pi*n)). - Vaclav Kotesovec, Feb 18 2023
D-finite with recurrence 2*n*a(n) +(-5*n+2)*a(n-1) +(-11*n+12)*a(n-2) +2*(-n+5)*a(n-3) +(-7*n+2)*a(n-4) +2*(-2*n+5)*a(n-5)=0. - R. J. Mathar, Mar 02 2023