A009747 E.g.f. tan(x)*sinh(x) (even powers only).

0, 2, 12, 142, 3192, 116282, 6219972, 458790022, 44625674352, 5534347077362, 852334810990332, 159592488559874302, 35703580441464231912, 9405575479317650316842, 2881823738166957609703092, 1016124476854507687644180982, 408525180980254462140262747872, 185768439922172208338308590282722

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: A351731 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