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A366558
G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^4.
5
1, 1, 0, 0, 1, 4, 6, 4, 5, 28, 84, 140, 162, 304, 1018, 2644, 4760, 7364, 15540, 42680, 102059, 195904, 356542, 782880, 1950844, 4467288, 9011156, 17960676, 39984254, 94642292, 212395260, 444063984, 931300500, 2082762572, 4796413292, 10681800072, 22892593021
OFFSET
0,6
FORMULA
a(n) = Sum_{k=0..floor(n/4)} binomial(3*k+1,n-4*k) * binomial(4*k,k)/(3*k+1).
a(n) = A366595(n) + A366595(n-1).
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(3*k+1, n-4*k)*binomial(4*k, k)/(3*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 13 2023
STATUS
approved