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A360861
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a(n) = Sum_{k=0..n} binomial(n, ceiling(k/2)) * binomial(n, floor(k/2)).
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2
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1, 2, 7, 22, 81, 281, 1058, 3830, 14605, 54127, 208110, 782761, 3027038, 11501478, 44668692, 170974710, 666220005, 2564271875, 10018268150, 38728479647, 151631858378, 588229029258, 2307174835212, 8975958379817, 35258881445606, 137501193282026, 540821096592028
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (1/2)*(binomial(2*n+1,n)+binomial(n,floor(n/2))^2). - Tani Akinari, Jul 12 2023
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MATHEMATICA
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A360861[n_]:=(Binomial[2n+1, n]+Binomial[n, Floor[n/2]]^2)/2;
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PROG
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(Python)
from math import comb
def A360861(n): return sum(comb(n, m:=k>>1)**2*(n-m)//(m+1) for k in range(1, n+1, 2)) + sum(comb(n, k>>1)**2 for k in range(0, n+1, 2)) # Chai Wah Wu, Feb 28 2023
(Maxima) a(n):=(1/2)*(binomial(2*n+1, n)+(binomial(n, floor(n/2)))^2); /* Tani Akinari, Jul 12 2023 */
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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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