A032115 - OEIS

%I #12 May 08 2020 09:42:48

%S 1,1,4,17,120,1169,13980,195649,3130288,56345057,1126900980,

%T 24791821361,595003712424,15470096522737,433162702636300,

%U 12994881079088609,415836194530835040,14138430614048390849,508983502105742069988,19341373080018198658897

%N "BIJ" (reversible, indistinct, labeled) transform of 1,3,5,7...

%H Andrew Howroyd, <a href="/A032115/b032115.txt">Table of n, a(n) for n = 0..200</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%F E.g.f.: (1 + 2*(1-2*x)*exp(x) - (1-2*x)^2*exp(2*x))/(2*(1-2*x)*exp(x)). - _Andrew Howroyd_, Sep 12 2018

%F a(n) ~ n! * 2^(n-1) * exp(-1/2). - _Vaclav Kotesovec_, Sep 13 2018

%F Conjecture: D-finite with recurrence a(n) +2*(-n-1)*a(n-1) +4*(n-1)*a(n-2) +2*a(n-3) +(-4*n+11)*a(n-4) +2*(n-4)*a(n-5)=0. - _R. J. Mathar_, May 08 2020

%o (PARI) seq(n)={my(p=1 + (2*x-1)*exp(x + O(x*x^n))); Vec(serlaplace((1-p^2/2)/(1-p)))} \\ _Andrew Howroyd_, Sep 12 2018

%K nonn

%O 0,3

%A _Christian G. Bower_

%E a(0)=1 prepended and terms a(18) and beyond from _Andrew Howroyd_, Sep 12 2018