A009739 E.g.f. tan(x)*exp(x).

0, 1, 2, 5, 12, 41, 142, 685, 3192, 19921, 116282, 887765, 6219972, 56126201, 458790022, 4776869245, 44625674352, 526589630881, 5534347077362, 72989204937125, 852334810990332, 12424192360405961, 159592488559874302, 2547879762929443405, 35703580441464231912

Offset: 0

Author

R. H. Hardin

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..484

Crossrefs

Cf. A003701.

Programs

Maple

G(x):=exp(x)*tan(x): f[0]:=G(x): for n from 1 to 54 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..22 ); # Zerinvary Lajos, Apr 05 2009
# Alternative:
S:= series(exp(x)*tan(x),x, 51):
seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Sep 22 2019

PARI

x='x+O('x^66); concat([0],Vec(serlaplace(tan(x)*exp(x)))) \\ Joerg Arndt, Apr 26 2013

Formula

a(2n) = A009747(n), a(2n+1) = A003719(n).

E.g.f.: exp(x)*tan(x). - Zerinvary Lajos, Apr 05 2009

G.f.: 1/(x-1)/Q(0), where Q(k)= 1 - 1/x - (k+1)*(k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Apr 26 2013

G.f.: x/(1-x)/Q(0), where Q(k)= 1 - x - x^2*(k+1)*(k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Apr 26 2013

G.f.: G(0)*x/(1-x)^2, where G(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - (1-x)^2/G(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Jan 23 2014

a(n) ~ 2^(3/2 + n)*(exp(Pi) - (-1)^n)*exp(-Pi/2 - n)*Pi^(-1/2 - n)*n^(1/2 + n). - Robert Israel, Sep 22 2019

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997