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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

Index entries for sequences related to 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-Fran├žois 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

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified November 18 13:22 EST 2018. Contains 317306 sequences. (Running on oeis4.)