|
| |
|
|
A006199
|
|
Bessel polynomial {y_n}'(-1).
(Formerly M3082)
|
|
4
|
|
|
|
0, 1, -3, 21, -185, 2010, -25914, 386407, -6539679, 123823305, -2593076255, 59505341676, -1484818160748, 40025880386401, -1159156815431055, 35891098374564105, -1183172853341759129, 41372997479943753582, -1529550505546305534414, 59608871544962952539335
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Absolute values give partitions into pairs.
|
|
|
REFERENCES
|
G. Kreweras and Y. Poupard, Sur les partitions en paires d'un ensemble fini totalement ordonné, Publications de l'Institut de Statistique de l'Université de Paris, 23 (1978), 57-74.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
G. C. Greubel, Table of n, a(n) for n = 1..400
Index entries for sequences related to Bessel functions or polynomials
|
|
|
FORMULA
|
a(n) = A000806(n) + (n-1) * A000806(n-1). - Sean A. Irvine, Jan 23 2017
From G. C. Greubel, Aug 14 2017: (Start)
a(n) = 2*n*(1/2)_{n} * (-2)^(n-1) * hyergeometric1f1(1-n; -2*n; -2), where (a)_{n} is the Pochhammer symbol.
E.g.f.: (1+2*x)^(-3/2)*( (1+2*x)^(3/2) - x*(1+2*x)^(1/2) - x -1) * exp(sqrt(1+2*x) - 1), for offset 0. (End)
G.f.: (x/(1-x)^3)*hypergeometric2f0(2,3/2; - ; -2*x/(1-x)^2), for offset 0. - G. C. Greubel, Aug 16 2017
|
|
|
MATHEMATICA
|
Join[{0}, Table[2*n*Pochhammer[1/2, n]*(-2)^(n - 1)* Hypergeometric1F1[1 - n, -2*n, -2], {n, 1, 50}]] (* G. C. Greubel, Aug 14 2017 *)
|
|
|
PROG
|
(PARI) for(n=0, 50, print1(sum(k=0, n-1, ((n+k)!/(k!*(n-k)!))*(-1/2)^k), ", ")) \\ G. C. Greubel, Aug 14 2017
|
|
|
CROSSREFS
|
Cf. A000806, A001514, A065707, A065920, A065921, A065922.
Sequence in context: A054879 A333090 A131763 * A083063 A012163 A012055
Adjacent sequences: A006196 A006197 A006198 * A006200 A006201 A006202
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
