A230961 Boustrophedon transform of factorials beginning with 1, cf. A000142.

1, 3, 11, 50, 273, 1746, 12823, 106462, 986689, 10103074, 113309991, 1381835454, 18209834849, 257911743506, 3907538236631, 63066584719982, 1080340925760129, 19577690297352258, 374214932301757255, 7524626434657416286, 158783753482817132065

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(A109449(n,k)*A000142(k+1): k=0..n).

E.g.f.: conjecture: (tan(x)+sec(x))/(1-2*x+x^2) = (1- 12*x/ (Q(0)+6*x+3*x^2))/(1-x)^2, 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! * n * (1+sin(1))/cos(1). - Vaclav Kotesovec, Jun 12 2015

Mathematica

T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
a[n_] := Sum[T[n, k] (k + 1)!, {k, 0, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 23 2019 *)

Prog

(Haskell)
a230961 n = sum $ zipWith (*) (a109449_row n) $ tail a000142_list
(Python)
from itertools import accumulate, count, islice
def A230961_gen(): # generator of terms
    blist, m = tuple(), 1
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist), initial=(m := m*i))))[-1]
A230961_list = list(islice(A230961_gen(), 40)) # Chai Wah Wu, Jun 12 2022

Crossrefs

Cf. A230960.

Sequence in context: A103466 A346762 A354323 * A203166 A000254 A081048

Adjacent sequences: A230958 A230959 A230960 * A230962 A230963 A230964

Keyword

nonn

Author

Reinhard Zumkeller, Nov 05 2013

Status

approved