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A366595
G.f. A(x) satisfies A(x) = 1 + x^4*(1+x)^3*A(x)^4.
3
1, 0, 0, 0, 1, 3, 3, 1, 4, 24, 60, 80, 82, 222, 796, 1848, 2912, 4452, 11088, 31592, 70467, 125437, 231105, 551775, 1399069, 3068219, 5942937, 12017739, 27966515, 66675777, 145719483, 298344501, 632955999, 1449806573, 3346606719, 7335193353, 15557399668
OFFSET
0,6
FORMULA
a(n) = Sum_{k=0..floor(n/4)} binomial(3*k,n-4*k) * binomial(4*k,k)/(3*k+1).
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(3*k, n-4*k)*binomial(4*k, k)/(3*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 14 2023
STATUS
approved