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A364622
G.f. satisfies A(x) = 1/(1-x)^2 + x^2*A(x)^4.
1
1, 2, 4, 12, 45, 182, 779, 3480, 16005, 75234, 359893, 1746268, 8573477, 42511646, 212587561, 1070897000, 5429174465, 27679933778, 141829437174, 729972918876, 3772160853821, 19563615260102, 101797930474515, 531293155760840, 2780515192595481, 14588670579665882
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n+4*k+1,6*k+1) * binomial(4*k,k) / (3*k+1).
MATHEMATICA
Table[Sum[Binomial[n + 4 k + 1, 6 k + 1]*Binomial[4 k, k]/(3 k + 1), {k, 0, Floor[n/2]}], {n, 0, 30}] (* Wesley Ivan Hurt, Jan 20 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(n+4*k+1, 6*k+1)*binomial(4*k, k)/(3*k+1));
CROSSREFS
Sequence in context: A238111 A165901 A074449 * A359328 A332235 A131387
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 30 2023
STATUS
approved