A365246 G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^2*A(x)^4).

1, 1, 2, 6, 22, 88, 370, 1613, 7230, 33117, 154330, 729369, 3487470, 16840346, 82007012, 402269702, 1985867630, 9858739759, 49187798158, 246506563980, 1240337033398, 6263601365616, 31734939452116, 161270637750264, 821802841072422, 4198348868249768

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = (1/(2*n+1)) * Sum_{k=0..floor(n/2)} binomial(n-k-1,k) * binomial(2*n+1,n-2*k).

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(n-k-1, k)*binomial(2*n+1, n-2*k))/(2*n+1);

Crossrefs

Cf. A364739, A365247.

Sequence in context: A199481 A049137 A287223 * A333080 A096267 A150264

Adjacent sequences: A365243 A365244 A365245 * A365247 A365248 A365249

Keyword

nonn

Author

Seiichi Manyama, Aug 28 2023

Status

approved