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

0,4

Links

Table of n, a(n) for n=0..28.

Formula

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

Prog

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

Crossrefs

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

Cf. A371891.

Sequence in context: A176966 A117977 A272870 * A362650 A176750 A030687

Adjacent sequences: A377455 A377456 A377457 * A377459 A377460 A377461

Keyword

nonn

Author

Seiichi Manyama, Dec 12 2024

Status

approved