A230960 Boustrophedon transform of factorials, cf. A000142.

1, 2, 5, 17, 73, 381, 2347, 16701, 134993, 1222873, 12279251, 135425553, 1627809401, 21183890469, 296773827547, 4453511170517, 71275570240417, 1211894559430065, 21816506949416611, 414542720924028441, 8291224789668806345, 174120672081098057341

Offset

0,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..400

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

Formula

a(n) = Sum_{k=0..n} A109449(n,k)*A000142(k).

E.g.f.: (tan(x)+sec(x))/(1-x) = (1- 12*x/(Q(0)+6*x+3*x^2))/(1-x), where Q(k) = 2*(4*k+1)*(32*k^2+16*k-x^2-6) - x^4*(4*k-1)*(4*k+7)/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Nov 18 2013

a(n) ~ n! * (1+sin(1))/cos(1). - Vaclav Kotesovec, Jun 12 2015

a(n) = Sum_{k=0..n} (k+1) * A092580(n,k). - Alois P. Heinz, Apr 27 2023

Mathematica

T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
a[n_] := Sum[T[n, k] k!, {k, 0, n}];
Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 02 2019 *)

Prog

(Haskell)
a230960 n = sum $ zipWith (*) (a109449_row n) a000142_list
(Python)
from itertools import count, islice, accumulate
def A230960_gen(): # generator of terms
    blist, m = tuple(), 1
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
        m *= i
A230960_list = list(islice(A230960_gen(), 30)) # Chai Wah Wu, Jun 11 2022

Crossrefs

Cf. A000142, A092580, A109449, A230961.

Sequence in context: A007779 A084161 A325294 * A102038 A002135 A260337

Adjacent sequences: A230957 A230958 A230959 * A230961 A230962 A230963

Keyword

nonn

Author

Reinhard Zumkeller, Nov 05 2013

Status

approved