A099598 Antidiagonal sums of array A099597.

1, 2, 4, 8, 19, 50, 162, 576, 2469, 11218, 59984, 331432, 2120663, 13784290, 102616622, 766648128, 6507054537, 54919451490, 523342287196, 4923469621256, 52040350449307, 539901936037202, 6268123599148282, 71087050308230912, 899190381412449645, 11066323452201287346

Offset

0,2

Links

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

Formula

From Paul Barry, May 26 2007: (Start)

a(n) = Sum_{k=0..n} C(n,k)*(floor(k/2)!)^2.

a(n) = Sum_{k=0..n} Sum{j=0..n-k} C(n-k,j)*C(k,j)j!^2. (End)

Mathematica

a[n_]:=Sum[Binomial[n, k]*(Floor[k/2]!)^2, {k, 0, n}]; Array[a, 26, 0] (* Stefano Spezia, Sep 06 2025 *)

Crossrefs

Sequence in context: A172383 A003081 A100133 * A269023 A387693 A173310

Adjacent sequences: A099595 A099596 A099597 * A099599 A099600 A099601

Keyword

nonn

Author

Ralf Stephan, Oct 28 2004

Extensions

a(23)-a(25) from Stefano Spezia, Sep 06 2025

Status

approved