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A378403
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+2*k,n-k).
1
1, 2, 10, 53, 290, 1632, 9349, 54231, 317538, 1872800, 11109520, 66213215, 396181229, 2378362248, 14318234311, 86409741438, 522592913026, 3166515425796, 19218755044816, 116820035092706, 711037336745440, 4333057549362840, 26434747722608191, 161433098212966732
OFFSET
0,2
FORMULA
a(n) = [x^n] (1 + x + x * (1 + x)^3)^n.
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(n+2*k, n-k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 25 2024
STATUS
approved