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A127394 Number of irreducible representations of Sp(2n,R) with same infinitesimal character as the trivial representation. 1
4, 18, 88, 460, 2544, 14776, 89632, 565392, 3695680, 24959776, 173752704, 1244125888, 9146568448, 68933546880, 531838104064, 4195358822656, 33800254620672, 277843218452992, 2328182040156160, 19870770461838336, 172610363453599744, 1525013813211609088 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

J. Adams and F. du Cloux, Algorithms for representation theory of real reductive groups, arXiv:math/0701166.

FORMULA

E.g.f.: exp(4*x+x^2). - corrected by Vaclav Kotesovec, Oct 19 2012

E.g.f. 2*(x+2)*(1 + (x+4)*x/(G(0)-x^2-4*x)) where G(k)= x^2 + 4*x + k + 1 - (x+4)*x*(k+1)/G(k+1); (continued fraction, Euler's 1st kind, 1-step). - Sergei N. Gladkovskii, Jul 12 2012

Recurrence: a(n) = 4*a(n-1) + 2*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 2^(n/2-1/2)*exp(2*sqrt(2*n)-n/2-2)*n^(n/2)*(1+7/6*sqrt(2)/sqrt(n)). - Vaclav Kotesovec, Oct 19 2012

MATHEMATICA

Rest[CoefficientList[Series[E^(4*x+x^2), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 19 2012 *)

PROG

(PARI) x='x+O('x^66);  Vec(serlaplace(2*(x+2)*exp(x*(x+4)))) /* Joerg Arndt, Jul 12 2012 */

CROSSREFS

Sequence in context: A260650 A006629 A068764 * A046984 A129323 A000305

Adjacent sequences:  A127391 A127392 A127393 * A127395 A127396 A127397

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 01 2007

STATUS

approved

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Last modified October 18 14:36 EDT 2018. Contains 316321 sequences. (Running on oeis4.)