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 A062162 #40 Jun 11 2022 01:19:47 %S A062162 1,0,0,1,0,5,10,61,280,1665,10470,73621,561660,4650425,41441530, %T A062162 395757181,4031082640,43626778785,499925138190,6046986040741, %U A062162 76992601769220,1029315335116745,14416214547400450,211085887742964301,3225154787165157400,51329932704636904305 %N A062162 Boustrophedon transform of (-1)^n. %C A062162 Inverse binomial transform of Euler numbers A000111. - _Paul Barry_, Jan 21 2005 %C A062162 a(n) = abs(sum of row n in A247453). - _Reinhard Zumkeller_, Sep 17 2014 %H A062162 Alois P. Heinz, <a href="/A062162/b062162.txt">Table of n, a(n) for n = 0..200</a> %H A062162 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>. %H A062162 Ludwig Seidel, <a href="https://babel.hathitrust.org/cgi/pt?id=hvd.32044092897461&view=1up&seq=175">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the <a href="https://www.hathitrust.org/accessibility">HATHI TRUST Digital Library</a>] %H A062162 Ludwig Seidel, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1877_0157-0187.pdf">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through <a href="https://de.wikipedia.org/wiki/ZOBODAT">ZOBODAT</a>] %H A062162 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>. %H A062162 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a> %F A062162 E.g.f.: exp(-x)*(tan(x) + sec(x)). - _Vladeta Jovovic_, Feb 11 2003 %F A062162 a(n) ~ 4*(2*n/Pi)^(n+1/2)/exp(n+Pi/2). - _Vaclav Kotesovec_, Oct 05 2013 %F A062162 G.f.: E(0)*x/(1+x) + 1/(1+x), where E(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - 2*(x*k-1)*(x*(k+1)-1)/E(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Jan 16 2014 %t A062162 CoefficientList[Series[E^(-x)*(Tan[x]+1/Cos[x]), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 05 2013 *) %t A062162 t[n_, 0] := (-1)^n; 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 A062162 (Sage) # Generalized algorithm of L. Seidel (1877) %o A062162 def A062162_list(n) : %o A062162 R = []; A = {-1:0, 0:0} %o A062162 k = 0; e = 1 %o A062162 for i in range(n) : %o A062162 Am = (-1)^i %o A062162 A[k + e] = 0 %o A062162 e = -e %o A062162 for j in (0..i) : %o A062162 Am += A[k] %o A062162 A[k] = Am %o A062162 k += e %o A062162 R.append(A[e*i//2]) %o A062162 return R %o A062162 A062162_list(22) # _Peter Luschny_, Jun 02 2012 %o A062162 (Haskell) %o A062162 a062162 = abs . sum . a247453_row -- _Reinhard Zumkeller_, Sep 17 2014 %o A062162 (Python) %o A062162 from itertools import islice, accumulate %o A062162 def A062162_gen(): # generator of terms %o A062162 blist, m = tuple(), -1 %o A062162 while True: %o A062162 yield (blist := tuple(accumulate(reversed(blist),initial=(m:=-m))))[-1] %o A062162 A062162_list = list(islice(A062162_gen(),20)) # _Chai Wah Wu_, Jun 10 2022 %Y A062162 Cf. A000111 (binomial transform). %Y A062162 Cf. A000667. %Y A062162 Cf. A247453. %K A062162 nonn,easy %O A062162 0,6 %A A062162 _Frank Ellermann_, Jun 10 2001