A378958 -id:A378958 - cp's OEIS frontend

A377458 G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 - A(x) + A(x)^4).

1, 1, 1, 4, 7, 29, 61, 256, 596, 2507, 6247, 26197, 68652, 286232, 780508, 3231060, 9102590, 37392935, 108279767, 441342883, 1308552478, 5292781266, 16018989626, 64315663716, 198213843417, 790252270626, 2474924176566, 9802205324516, 31142246753638

Offset: 0

Seiichi Manyama, Dec 12 2024

nonn

Cf. A317133, A364759, A377706, A378958, A378920.

Cf. A371891.

a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(2*n-4*k, n-k-1))/n);

a(n) = (1/n) * Sum_{k=0..n} (-1)^k * binomial(n,k) * binomial(2*n-4*k,n-k-1) for n > 0.

A377706 G.f. A(x) satisfies A(x) = 1 + x/A(x)^3 * (1 - A(x) + A(x)^4).

Original entry on oeis.org

1, 1, 0, 3, -6, 28, -105, 444, -1897, 8338, -37305, 169471, -779537, 3623500, -16993990, 80316081, -382136133, 1828896726, -8798796709, 42528048930, -206413678447, 1005623593109, -4916026689088, 24106987842416, -118551374861525, 584526569727010, -2888995759466360

Offset: 0

Seiichi Manyama, Dec 12 2024

sign

Cf. A317133, A364759, A377458, A378958, A378920.

Cf. A371890.

a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(n-4*k, n-k-1))/n);

a(n) = (1/n) * Sum_{k=0..n} (-1)^k * binomial(n,k) * binomial(n-4*k,n-k-1) for n > 0.

cp's OEIS Frontend

A377458 G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 - A(x) + A(x)^4).

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