A134184 A transform of the central binomial coefficients A001405.

1, 1, 3, 7, 17, 43, 109, 279, 721, 1871, 4881, 12783, 33585, 88495, 233745, 618719, 1640833, 4358719, 11595841, 30890751, 82391297, 219995007, 588004737, 1573072383, 4211960065, 11286490879, 30265474305, 81213330175, 218061109505, 585844009727, 1574788488449, 4235298883071

Offset

0,3

Comments

Hankel transform is A134185.

Links

Table of n, a(n) for n=0..31.

Formula

G.f.: g(x(1+x)) where g(x) is the g.f. of A001405.

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

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

Mathematica

a[n_]:=Sum[Binomial[k, n-k]*Binomial[k, Floor[k/2]], {k, 0, n}]; Array[a, 32, 0] (* Stefano Spezia, Dec 26 2025 *)

Crossrefs

Cf. A001405, A134185.

Sequence in context: A238824 A340766 A161943 * A142975 A211277 A114589

Adjacent sequences: A134181 A134182 A134183 * A134185 A134186 A134187

Keyword

easy,nonn

Author

Paul Barry, Oct 11 2007

Extensions

a(27)-a(31) from Stefano Spezia, Dec 26 2025

Status

approved