A032115 "BIJ" (reversible, indistinct, labeled) transform of 1,3,5,7...

1, 1, 4, 17, 120, 1169, 13980, 195649, 3130288, 56345057, 1126900980, 24791821361, 595003712424, 15470096522737, 433162702636300, 12994881079088609, 415836194530835040, 14138430614048390849, 508983502105742069988, 19341373080018198658897

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

C. G. Bower, Transforms (2)

Formula

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

a(n) ~ n! * 2^(n-1) * exp(-1/2). - Vaclav Kotesovec, Sep 13 2018

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

Prog

(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

Crossrefs

Sequence in context: A360879 A206353 A260694 * A054927 A307794 A071138

Adjacent sequences: A032112 A032113 A032114 * A032116 A032117 A032118

Keyword

nonn

Author

Christian G. Bower

Extensions

a(0)=1 prepended and terms a(18) and beyond from Andrew Howroyd, Sep 12 2018

Status

approved