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
FORMULA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 05 2013
STATUS
approved