A378069 a(n) = Sum_{k=0..n} binomial(n, floor(k/2 - 1/2)) * binomial(n, ceiling(k/2 - 1/2)).
0, 1, 3, 13, 45, 181, 658, 2605, 9705, 38251, 144606, 569317, 2173262, 8556822, 32890068, 129565485, 500583105, 1973295775, 7654363750, 30194784763, 117497078842, 463820452602, 1809540528588, 7147843461733, 27946421773270, 110458073192026, 432648616232028
Offset: 0
Programs
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Maple
a := n -> add(binomial(n, floor(k/2 - 1/2))*binomial(n, ceil(k/2 - 1/2)), k=0..n): seq(a(n), n = 0..26);