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A230960 Boustrophedon transform of factorials, cf. A000142.

%I A230960 #24 Apr 27 2023 14:24:59
%S A230960 1,2,5,17,73,381,2347,16701,134993,1222873,12279251,135425553,
%T A230960 1627809401,21183890469,296773827547,4453511170517,71275570240417,
%U A230960 1211894559430065,21816506949416611,414542720924028441,8291224789668806345,174120672081098057341
%N A230960 Boustrophedon transform of factorials, cf. A000142.
%H A230960 Reinhard Zumkeller, <a href="/A230960/b230960.txt">Table of n, a(n) for n = 0..400</a>
%H A230960 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%H A230960 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 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).
%H A230960 Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon_transform</a>
%H A230960 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A230960 a(n) = Sum_{k=0..n} A109449(n,k)*A000142(k).
%F A230960 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
%F A230960 a(n) ~ n! * (1+sin(1))/cos(1). - _Vaclav Kotesovec_, Jun 12 2015
%F A230960 a(n) = Sum_{k=0..n} (k+1) * A092580(n,k). - _Alois P. Heinz_, Apr 27 2023
%t A230960 T[n_, k_] := (n!/k!) SeriesCoefficient[(1 + Sin[x])/Cos[x], {x, 0, n - k}];
%t A230960 a[n_] := Sum[T[n, k] k!, {k, 0, n}];
%t A230960 Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Jul 02 2019 *)
%o A230960 (Haskell)
%o A230960 a230960 n = sum $ zipWith (*) (a109449_row n) a000142_list
%o A230960 (Python)
%o A230960 from itertools import count, islice, accumulate
%o A230960 def A230960_gen(): # generator of terms
%o A230960     blist, m = tuple(), 1
%o A230960     for i in count(1):
%o A230960         yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
%o A230960         m *= i
%o A230960 A230960_list = list(islice(A230960_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A230960 Cf. A000142, A092580, A109449, A230961.
%K A230960 nonn
%O A230960 0,2
%A A230960 _Reinhard Zumkeller_, Nov 05 2013