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A000745 Boustrophedon transform of squares.

%I A000745 #40 Jun 12 2022 12:13:48
%S A000745 1,5,18,57,180,617,2400,10717,54544,312353,1988104,13921501,106350816,
%T A000745 880162337,7844596536,74910367309,763030711936,8257927397569,
%U A000745 94628877364936,1144609672707741,14573622985067744,194834987492011649,2728787718495477144,39955604972310966797
%N A000745 Boustrophedon transform of squares.
%H A000745 Reinhard Zumkeller, <a href="/A000745/b000745.txt">Table of n, a(n) for n = 0..400</a>
%H A000745 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%H A000745 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996) 44-54 (<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 A000745 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A000745 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>
%H A000745 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A000745 a(n) ~ n! * (6 + Pi + 4/Pi) * exp(Pi/2) * 2^n / Pi^n. - _Vaclav Kotesovec_, Jun 12 2015
%F A000745 E.g.f.: exp(x)*(x^2 + 3*x + 1)*(1+sin(x))/cos(x). - _Vaclav Kotesovec_, Jun 12 2015
%t A000745 CoefficientList[Series[E^(x)*(x^2+3*x+1)*(1+Sin[x])/Cos[x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jun 12 2015 *)
%t A000745 t[n_, 0] := (n + 1)^2; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 30, 0] (* _Jean-François Alcover_, Feb 12 2016 *)
%o A000745 (Haskell)
%o A000745 a000745 n = sum $ zipWith (*) (a109449_row n) $ tail a000290_list
%o A000745 -- _Reinhard Zumkeller_, Nov 03 2013
%o A000745 (Python)
%o A000745 from itertools import accumulate, count, islice
%o A000745 def A000745_gen(): # generator of terms
%o A000745     blist, c = tuple(), 1
%o A000745     for i in count(1):
%o A000745         yield (blist := tuple(accumulate(reversed(blist),initial=c)))[-1]
%o A000745         c += 2*i+1
%o A000745 A000745_list = list(islice(A000745_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A000745 Cf. A000290, A000697.
%K A000745 nonn
%O A000745 0,2
%A A000745 _N. J. A. Sloane_