A073767 Bateman polynomial values n!*Z_n(-1).

1, 3, 20, 188, 2214, 30922, 495816, 8931960, 177999366, 3878476418, 91558971096, 2324529942088, 63084714688540, 1820757355281828, 55645592361311504, 1794034726184859120, 60817844748284215110, 2161623389394872099250, 80346564637248427227960

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

M. C. Fasenmyer, A note on pure recurrence relations, Amer. Math. Monthly 56, (1949), 14-17. Math. Rev. 10,704b.

Formula

a(n) = n!(Sum k=0..n (n+k)!/(k!^3(n-k)!)) = n!*F(-n, n+1;1, 1;-1).

n(2n-3)a(n) = (2n-1)(3n^2-2n-4)a(n-1)-(2n-3)(3n^2-10n+4)(n-1)a(n-2)+(n-1)(2n-1)(n-2)^3a(n-3).

E.g.f.: exp(2*x/(x-1)^2)*BesselI(0,2*x/(x-1)^2)/(1-x). - Mark van Hoeij, Oct 24 2011

a(n) ~ n^(n-1/6) * exp(3*n^(2/3)-n-1/3) / sqrt(6*Pi) * (1 + 1/n^(1/3) + 61/(90*n^(2/3))). - Vaclav Kotesovec, Feb 25 2014

Mathematica

Table[n!*Sum[(n+k)!/(n-k)!/k!^3, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 25 2014 *)

Prog

(PARI) a(n)=if(n<0, 0, n!*sum(k=0, n, (n+k)!/(n-k)!/k!^3))
(Sage)
A073767 = lambda n: factorial(n)*hypergeometric([-n, n+1], [1, 1], -1)
[round(A073767(n).n(100)) for n in (0..18)] # Peter Luschny, Sep 18 2014

Crossrefs

Cf. A073768.

Sequence in context: A065980 A302581 A305460 * A226349 A208975 A286794

Adjacent sequences: A073764 A073765 A073766 * A073768 A073769 A073770

Keyword

nonn

Author

Michael Somos, Aug 08 2002

Status

approved