%I #29 Apr 20 2023 15:04:27
%S 1,1,2,7,19,52,172,550,1782,5845,18508,56345,164157,454518,1196924,
%T 3003750,7198311,16523847,36447873,77478005,159172517,316874035,
%U 612729396,1153359711,2117566545,3798941401,6670327291,11479693332,19390588953,32185179449,52553840336
%N Expansion of Molien series for 16-dimensional complex Clifford group of genus 4 and order 97029351014400.
%C Oura gives an explicit formula for the Molien series that produces A027672; the present sequence is the subsequence formed from the terms whose exponents are multiples of 8 (that is, every other term of A027672). In other words, the present Molien series is (f(x)+f(z*x))/2, where z = exp(2*Pi*I/8) and f(x) is the Molien series for the group H_4 given explicitly by Oura in Theorem 4.1.
%H Ray Chandler, <a href="/A051354/b051354.txt">Table of n, a(n) for n = 0..1000</a>
%H Ray Chandler, <a href="/A051354/a051354.txt">Mathematica program</a>
%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%H M. Oura, <a href="http://projecteuclid.org/euclid.ojm/1200787332">The dimension formula for the ring of code polynomials in genus 4</a>, Osaka J. Math. 34 (1997), 53-72.
%H <a href="/index/Rec#order_120">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, 0, -3, 5, -2, -1, -1, 8, -7, -2, 2, 7, -7, -3, 1, 9, -11, 4, 3, 5, -9, -1, 0, 13, -15, 0, 4, 6, -9, 0, 8, 9, -18, -2, 12, -4, -4, -3, 6, 6, -8, -7, 18, -1, -6, -13, 13, 6, -14, -10, 30, -10, -10, -4, 22, -5, -6, -15, 28, -15, -6, -5, 22, -4, -10, -10, 30, -10, -14, 6, 13, -13, -6, -1, 18, -7, -8, 6, 6, -3, -4, -4, 12, -2, -18, 9, 8, 0, -9, 6, 4, 0, -15, 13, 0, -1, -9, 5, 3, 4, -11, 9, 1, -3, -7, 7, 2, -2, -7, 8, -1, -1, -2, 5, -3, 0, -2, 3, -1).
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%F a(n) = A027672(2*n).
%e 1 + t^8 + 2*t^16 + 7*t^24 + 19*t^32 + 52*t^40 + 172*t^48 + ...
%t See link for Mathematica program.
%Y Cf. A027672, A003956, A008621, A008718, A024186, A008620, A028288, A043330.
%K nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_
%E Edited by _Georg Fischer_, Jan 24 2021