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A367047
G.f. satisfies A(x) = 1 - x^3 + x*A(x)^4.
1
1, 1, 4, 21, 136, 941, 6864, 52006, 405312, 3228654, 26170764, 215166638, 1789998808, 15040070843, 127450104568, 1087988783356, 9347556057040, 80766068931498, 701359680126592, 6117887649100980, 53581405635501276, 470988258063461393
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(3*(n-3*k)+1,k) * binomial(4*(n-3*k),n-3*k)/(3*(n-3*k)+1).
PROG
(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(3*(n-3*k)+1, k)*binomial(4*(n-3*k), n-3*k)/(3*(n-3*k)+1));
CROSSREFS
Cf. A367043.
Sequence in context: A001909 A205077 A292928 * A209881 A288869 A052852
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 03 2023
STATUS
approved