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A366555
G.f. A(x) satisfies A(x) = 1 + x + x^3*A(x)^3.
6
1, 1, 0, 1, 3, 3, 4, 15, 30, 42, 99, 255, 475, 915, 2232, 4977, 9945, 21945, 51093, 110634, 238005, 542341, 1227390, 2696841, 6035886, 13770402, 31001133, 69485295, 157945293, 359888373, 814699002, 1850816823, 4231092060, 9659302380, 22028018679
OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(2*k+1,n-3*k) * binomial(3*k,k)/(2*k+1).
a(n) = A366591(n) + A366591(n-1).
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(2*k+1, n-3*k)*binomial(3*k, k)/(2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 13 2023
STATUS
approved