This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A000754 #47 Jun 12 2022 12:01:03 %S A000754 1,4,12,33,96,317,1218,5425,27608,158129,1006574,7048657,53847420, %T A000754 445643681,3971876930,37928628529,386337833232,4181155148673, %U A000754 47912508680086,579538956964241,7378919177090244,98648882783190305 %N A000754 Boustrophedon transform of odd numbers. %H A000754 Reinhard Zumkeller, <a href="/A000754/b000754.txt">Table of n, a(n) for n = 0..400</a> %H A000754 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>. %H A000754 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 A000754 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>. %H A000754 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>. %H A000754 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a> %F A000754 From _Reinhard Zumkeller_, Nov 02 2013: (Start) %F A000754 a(n) = Sum_{k=0..n} A116666(n+1,k)*A000111(n-k). %F A000754 a(n) = Sum_{k=0..n} A109449(n,k)*(2*k + 1). (End) %F A000754 E.g.f.: (sec(x) + tan(x))*exp(x)*(2*x + 1). - _Sergei N. Gladkovskii_, Oct 30 2014 %F A000754 a(n) ~ n! * (Pi+1) * exp(Pi/2) * 2^(n+2) / Pi^(n+1). - _Vaclav Kotesovec_, Oct 30 2014 %t A000754 CoefficientList[Series[(Sec[x]+Tan[x])*E^x*(2*x+1), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 30 2014 after _Sergei N. Gladkovskii_ *) %t A000754 t[n_, 0] := 2n + 1; 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 A000754 (Haskell) %o A000754 a000754 n = sum $ zipWith (*) (a109449_row n) [1, 3 ..] %o A000754 -- _Reinhard Zumkeller_, Nov 02 2013 %o A000754 (Python) %o A000754 from itertools import accumulate, count, islice %o A000754 def A000754_gen(): # generator of terms %o A000754 blist = tuple() %o A000754 for i in count(1,2): %o A000754 yield (blist := tuple(accumulate(reversed(blist),initial=i)))[-1] %o A000754 A000754_list = list(islice(A000754_gen(),40)) # _Chai Wah Wu_, Jun 12 2022 %Y A000754 Cf. A005408. %K A000754 nonn,nice,easy %O A000754 0,2 %A A000754 _N. J. A. Sloane_