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A062162 Boustrophedon transform of (-1)^n. 8
1, 0, 0, 1, 0, 5, 10, 61, 280, 1665, 10470, 73621, 561660, 4650425, 41441530, 395757181, 4031082640, 43626778785, 499925138190, 6046986040741, 76992601769220, 1029315335116745, 14416214547400450, 211085887742964301, 3225154787165157400, 51329932704636904305 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Inverse binomial transform of Euler numbers A000111. - Paul Barry, Jan 21 2005

a(n) = abs(sum of row n in A247453). - Reinhard Zumkeller, Sep 17 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

Peter Luschny, An old operation on sequences: the Seidel transform

Index entries for sequences related to boustrophedon transform

FORMULA

E.g.f.: exp(-x)*(tan(x) + sec(x)). - Vladeta Jovovic, Feb 11 2003

a(n) ~ 4*(2*n/Pi)^(n+1/2)/exp(n+Pi/2). - Vaclav Kotesovec, Oct 05 2013

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

MATHEMATICA

CoefficientList[Series[E^(-x)*(Tan[x]+1/Cos[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 05 2013 *)

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-Fran├žois Alcover, Feb 12 2016 *)

PROG

(Sage) # Generalized algorithm of L. Seidel (1877)

def A062162_list(n) :

    R = []; A = {-1:0, 0:0}

    k = 0; e = 1

    for i in range(n) :

        Am = (-1)^i

        A[k + e] = 0

        e = -e

        for j in (0..i) :

            Am += A[k]

            A[k] = Am

            k += e

        R.append(A[e*i//2])

    return R

A062162_list(22) # Peter Luschny, Jun 02 2012

(Haskell)

a062162 = abs . sum . a247453_row -- Reinhard Zumkeller, Sep 17 2014

CROSSREFS

Cf. A000111 (binomial transform).

Cf. A000667.

Cf. A247453.

Sequence in context: A072309 A240647 A061518 * A062848 A054884 A218540

Adjacent sequences:  A062159 A062160 A062161 * A062163 A062164 A062165

KEYWORD

nonn,easy

AUTHOR

Frank Ellermann, Jun 10 2001

STATUS

approved

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Last modified November 17 20:53 EST 2018. Contains 317278 sequences. (Running on oeis4.)