A373708 -id:A373708 - cp's OEIS frontend

A373706 Expansion of 1/(1 - x * (1 + x^4)^2).

1, 1, 1, 1, 1, 3, 5, 7, 9, 12, 19, 30, 45, 64, 91, 134, 201, 300, 440, 641, 939, 1386, 2050, 3021, 4437, 6516, 9588, 14128, 20811, 30624, 45042, 66268, 97545, 143604, 211368, 311040, 457704, 673605, 991437, 1459215, 2147563, 3160516, 4651330, 6845572, 10075042

Offset: 0

Seiichi Manyama, Jun 14 2024

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,2,0,0,0,1).

Cf. A005711, A193147, A373708.

a(n) = sum(k=0, 2*n\9, binomial(2*n-8*k, k));

a(n) = a(n-1) + 2*a(n-5) + a(n-9) for n > 8.
a(n) = Sum_{k=0..floor(2*n/9)} binomial(2*n-8*k,k).
a(n) = A005711(2*n-1) for n > 0.

A373707 Expansion of e.g.f. exp(x * (1 + x^3)^2).

Original entry on oeis.org

1, 1, 1, 1, 49, 241, 721, 6721, 124321, 913249, 4243681, 94818241, 1640604241, 14642181841, 131026944049, 3669304504321, 62536989802561, 627395160826561, 10818406189690561, 308036857749752449, 5219006583104930161, 65146235714284117681

Offset: 0

Seiichi Manyama, Jun 14 2024

nonn

Cf. A361278, A373578, A373708.
Cf. A190875, A373522, A373523.
Cf. A373680.

a(n) = n!*sum(k=0, 2*n\7, binomial(2*n-6*k, k)/(n-3*k)!);

a(n) = n! * Sum_{k=0..floor(2*n/7)} binomial(2*n-6*k,k)/(n-3*k)!.
a(n) == 1 (mod 48).
a(n) = a(n-1) + 8*(n-1)*(n-2)*(n-3)*a(n-4) + 7*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*a(n-7).

cp's OEIS Frontend

A373706 Expansion of 1/(1 - x * (1 + x^4)^2).

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