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A373719
a(n) = Sum_{k=0..floor(n^2/(2*n+1))} binomial(n * (n-2*k),k).
1
1, 1, 1, 4, 9, 26, 91, 281, 1105, 4105, 16576, 70643, 301405, 1382928, 6363876, 30605836, 150820769, 758835104, 3941917840, 20787546715, 112615930451, 620969188400, 3492709446326, 20034747631656, 116780977502105, 693539635192626, 4181549476945504, 25627647913369903
OFFSET
0,4
FORMULA
a(n) = [x^n] 1/(1 - x * (1 + x^2)^n).
PROG
(PARI) a(n) = sum(k=0, n^2\(2*n+1), binomial(n*(n-2*k), k));
CROSSREFS
Main diagonal of A373717.
Cf. A099237.
Sequence in context: A291064 A145855 A363448 * A354604 A240042 A099615
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 15 2024
STATUS
approved