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 A000734 Boustrophedon transform of 1,1,2,4,8,16,32,... 5
 1, 2, 5, 15, 49, 177, 715, 3255, 16689, 95777, 609875, 4270695, 32624329, 269995377, 2406363835, 22979029335, 234062319969, 2533147494977, 29027730898595, 351112918079175, 4470508510495609, 59766296291090577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A062272. - Paul Barry, Jan 21 2005 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 on transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps). N. J. A. Sloane, Transforms Wikipedia, Boustrophedon_transform FORMULA E.g.f.: (1+exp(2x))(sec(x)+tan(x))/2. - Paul Barry, Jan 21 2005 a(n) ~ n! * (1+exp(Pi)) * (2/Pi)^(n+1). - Vaclav Kotesovec, Oct 07 2013 MATHEMATICA CoefficientList[Series[(1+E^(2*x))*(Sec[x]+Tan[x])/2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 07 2013 *) t[n_, 0] := If[n == 0, 1, 2^(n-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 *) PROG (Sage) # Algorithm of L. Seidel (1877) def A000734_list(n) :     A = {-1:0, 0:1}; R = []     k = 0; e = 1; Bm = 1     for i in range(n) :         Am = Bm         A[k + e] = 0         e = -e         for j in (0..i) :             Am += A[k]             A[k] = Am             k += e         Bm += Bm         R.append(A[e*i//2]/2)     return R A000734_list(22) # Peter Luschny, Jun 02 2012 (Haskell) a000734 n = sum \$ zipWith (*) (a109449_row n) (1 : a000079_list) -- Reinhard Zumkeller, Nov 04 2013 CROSSREFS Cf. A109449, A000079, A000752. Sequence in context: A149942 A149943 A079146 * A148366 A005751 A202182 Adjacent sequences:  A000731 A000732 A000733 * A000735 A000736 A000737 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 17 15:16 EST 2019. Contains 319225 sequences. (Running on oeis4.)