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A273020
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a(n) = Sum_{k=0..n} C(n,k)*((-1)^n*(C(k,n-k)-C(k,n-k-1))+C(n-k,k+1)).
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2
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1, 1, 3, 5, 19, 39, 141, 321, 1107, 2675, 8953, 22483, 73789, 190345, 616227, 1621413, 5196627, 13882947, 44152809, 119385663, 377379369, 1030434069, 3241135527, 8921880135, 27948336381, 77459553549, 241813226151, 674100041501, 2098240353907, 5878674505303, 18252025766941
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = JacobiP(n, 1, -n-3/2, -7)/(n+1) + GegenbauerC(n-1, -n, -1/2), with a(0) = 1.
a(n) = hypergeom([-n,1/2], [2], 4) + n*hypergeom([-n/2+1,-n/2+1/2], [2], 4).
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MAPLE
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seq(simplify(hypergeom([-n, 1/2], [2], 4) + n*hypergeom([-n/2+1, -n/2+1/2], [2], 4)), n=0..30);
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MATHEMATICA
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Table[ JacobiP[n, 1, -n-3/2, -7]/(n+1) + GegenbauerC[n-1, -n, -1/2], {n, 0, 30} ]
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PROG
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(Sage)
def A():
a, b, c, d, n = 0, 1, 1, -1, 1
yield 1
while True:
yield d + b*(1-(-1)^n)
n += 1
a, b = b, (3*(n-1)*n*a+(2*n-1)*n*b)//((n+1)*(n-1))
c, d = d, (3*(n-1)*c-(2*n-1)*d)//n
print([next(A273020) for _ in range(31)])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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