A372021 G.f. A(x) satisfies A(x) = ( 1 + 4*x/(1 - x*A(x))^2 )^(1/2).

1, 2, 2, 10, 18, 90, 210, 1010, 2754, 12754, 38626, 173434, 566034, 2481578, 8556722, 36848994, 132406274, 562781730, 2086628034, 8786281322, 33372861074, 139609461370, 540319600530, 2250413871698, 8838703576002, 36709888093938, 145870057771938

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

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

Prog

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

Crossrefs

Cf. A372022.

Sequence in context: A265199 A294755 A102446 * A348957 A303565 A291856

Adjacent sequences: A372018 A372019 A372020 * A372022 A372023 A372024

Keyword

nonn

Author

Seiichi Manyama, Apr 16 2024

Status

approved