A350325 Binomial transform of A339399(n).

1, 2, 4, 9, 20, 44, 97, 213, 460, 971, 2009, 4107, 8366, 17075, 34979, 71855, 147754, 303726, 623872, 1280778, 2628983, 5396437, 11074436, 22707284, 46484364, 94941993, 193400116, 392918836, 796439093, 1611656388, 3258188320, 6585057484, 13312190228, 26926301891

Offset

0,2

Links

Table of n, a(n) for n=0..33.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A339399(n-k+1).

Mathematica

a[n_] := (1 + (-1)^n) (1 + Floor[Sqrt[2 n - 1 - (-1)^n]])/2 - ((2 n + 1 - (-1)^n)/2 - 2 Sum[Floor[(k + 1)/2], {k, -1 + Floor[Sqrt[2 n - 2 - (-1)^n]]}]) (-1)^n/2; Table[Sum[Binomial[n, i]*a[n - i + 1], {i, 0, n}], {n, 0, 40}]

Crossrefs

Cf. A339399.

Sequence in context: A130587 A129988 A035530 * A141016 A008998 A024736

Adjacent sequences: A350322 A350323 A350324 * A350326 A350327 A350328

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 24 2021

Status

approved