A230957 Boustrophedon transform of partition numbers A000009.

1, 2, 4, 10, 29, 94, 364, 1621, 8255, 47277, 300962, 2107479, 16099922, 133243363, 1187555333, 11340314638, 115511502857, 1250127378307, 14325404633040, 173276880401035, 2206229765086251, 29495119298584886, 413097874985119467, 6048684327982905454

Offset: 0

Author

Reinhard Zumkeller, Nov 03 2013

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..150
• Peter Luschny, An old operation on sequences: the Seidel transform
• J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).
• Wikipedia, Boustrophedon transform
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000751.

Programs

Haskell

a230957 n = sum $ zipWith (*) (a109449_row n) a000009_list

Mathematica

T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
a[n_] := Sum[T[n, k] PartitionsQ[k], {k, 0, n}];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jul 23 2019 *)

Formula

a(n) = sum(A109449(n,k)*A000009(k): k=0..n).