|
|
A065948
|
|
Bessel polynomial {y_n}''(-3).
|
|
1
|
|
|
0, 0, 6, -240, 9540, -415590, 20134590, -1082674404, 64221641820, -4173853100670, 295282282905720, -22605059036265420, 1862664627479732076, -164425432052147568120, 15483794266369962976170, -1549617160894627918342620, 164264715996348003982855020
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
REFERENCES
|
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 4*n*(n - 1)*(1/2)_{n}*(-6)^(n - 2)* hypergeometric1f1(2 - n; -2*n; -2/3), where (a)_{n} is the Pochhammer symbol.
E.g.f.: (-1/81)*(1 + 6*x)^(-5/2)*((-99*x^2 - 54*x - 4)*sqrt(1 + 6*x) + (-54*x^3 + 66*x + 4))*exp(-(1 - sqrt(1 + 6*x))/3). (End)
G.f.: (6*x^2/(1-x)^5)*hypergeometric2f0(3,5/2; - ; -6*x/(1-x)^2). - G. C. Greubel, Aug 16 2017
|
|
MATHEMATICA
|
Join[{0, 0}, Table[4*n*(n - 1)*Pochhammer[1/2, n]*(-6)^(n - 2)* Hypergeometric1F1[2 - n, -2*n, -2/3], {n, 2, 50}]] (* G. C. Greubel, Aug 15 2017 *)
|
|
PROG
|
(PARI) for(n=0, 50, print1(sum(k=0, n-2, ((n+k+2)!/(4*k!*(n-k-2)!))*(-3/2)^k ), ", ")) \\ G. C. Greubel, Aug 15 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|