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 A000660 Boustrophedon transform of 1,1,2,3,4,5,... 3
 1, 2, 5, 14, 41, 136, 523, 2330, 11857, 67912, 432291, 3027166, 23125673, 191389108, 1705788659, 16289080922, 165919213089, 1795666675824, 20576824369027, 248892651678198, 3168999664907705, 42366404751871660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 a(n) = Sum_{k=0..n} A109449(n,k)*A028310(k). - Reinhard Zumkeller, Nov 04 2013 E.g.f.:  (x*exp(x) + 1)*(sec(x) + tan(x)). - Sergei N. Gladkovskii, Oct 28 2014 a(n) = A231179(n) + A000111(n). - Sergei N. Gladkovskii, Oct 28 2014 a(n) ~ n! * (2 + Pi*exp(Pi/2)) * (2/Pi)^(n+1). - Vaclav Kotesovec, Jun 12 2015 MAPLE seq(coeff(series(factorial(n)*(x*exp(x)+1)*(sec(x)+tan(x)), x, n+1), x, n), n=0..25); # Muniru A Asiru, Jul 30 2018 MATHEMATICA a[n_] := n! SeriesCoefficient[(1+x Exp[x])(1+Sin[x])/Cos[x], {x, 0, n}]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jul 30 2018, after Sergei N. Gladkovskii *) PROG (Sage) # Algorithm of L. Seidel (1877) def A000660_list(n) :     R = []; A = {-1:0, 0:1}     k = 0; e = 1     for i in range(n) :         Am = i         A[k + e] = 0         e = -e         for j in (0..i) :             Am += A[k]             A[k] = Am             k += e         print [A[z] for z in (-i//2..i//2)]         R.append(A[e*i//2])     return R A000660_list(10) # Peter Luschny, Jun 02 2012 (Haskell) a000660 n = sum \$ zipWith (*) (a109449_row n) (1 : [1..]) -- Reinhard Zumkeller, Nov 04 2013 CROSSREFS Sequence in context: A148322 A148323 A148324 * A148325 A281594 A174176 Adjacent sequences:  A000657 A000658 A000659 * A000661 A000662 A000663 KEYWORD nonn,changed AUTHOR STATUS approved

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Last modified October 20 07:33 EDT 2019. Contains 328252 sequences. (Running on oeis4.)