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

Author

R. H. Hardin

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..240
• Peter Luschny, An old operation on sequences: the Seidel transform

Crossrefs

Bisection of A009739 and (apparently) A062161.

Programs

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 *)

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

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

Formula

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

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997