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A009747 E.g.f. tan(x)*sinh(x) (even powers only). 9
0, 2, 12, 142, 3192, 116282, 6219972, 458790022, 44625674352, 5534347077362, 852334810990332, 159592488559874302, 35703580441464231912, 9405575479317650316842, 2881823738166957609703092, 1016124476854507687644180982, 408525180980254462140262747872, 185768439922172208338308590282722 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..240

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

FORMULA

a(n) ~ (2*n)! * 4^(n+1) * sinh(Pi/2) / Pi^(2*n+1). - Vaclav Kotesovec, Jan 24 2015

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Sinh[x]*Tan[x], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Jan 24 2015 *)

PROG

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

def A009747_list(n) :

    R = []; A = {-1:0, 0:0}

    k = 0; e = 1

    for i in range(2*n) :

        Am = 1 if e == -1 else 0

        A[k + e] = 0

        e = -e

        for j in (0..i) :

            Am += A[k]

            A[k] = Am

            k += e

        if e == -1 : R.append(A[-i//2])

    return R

A009747_list(10) # Peter Luschny, Jun 02 2012

(PARI) x='x+O('x^66); v=Vec(serlaplace(tan(x)*sinh(x))); concat([0], vector(#v\2, n, v[2*n-1])) \\ Joerg Arndt, Apr 26 2013

CROSSREFS

Bisection of A009739 and (apparently) A062161.

Sequence in context: A275829 A240387 A087800 * A208866 A334174 A067601

Adjacent sequences:  A009744 A009745 A009746 * A009748 A009749 A009750

KEYWORD

nonn

AUTHOR

R. H. Hardin

EXTENSIONS

Extended and signs tested by Olivier Gérard, Mar 15 1997

STATUS

approved

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Last modified September 20 10:24 EDT 2020. Contains 337264 sequences. (Running on oeis4.)