|
| |
|
|
A073767
|
|
Bateman polynomial values n!Z_n(-1).
|
|
1
| |
|
|
1, 3, 20, 188, 2214, 30922, 495816, 8931960, 177999366, 3878476418, 91558971096, 2324529942088, 63084714688540, 1820757355281828, 55645592361311504, 1794034726184859120, 60817844748284215110, 2161623389394872099250
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| 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
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, n!*sum(k=0, n, (n+k)!/(n-k)!/k!^3))
|
|
|
CROSSREFS
| Cf. A073768.
Sequence in context: A129840 A085390 A065980 * A176043 A108206 A120485
Adjacent sequences: A073764 A073765 A073766 * A073768 A073769 A073770
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Michael Somos, Aug 08 2002
|
| |
|
|
