A030535 Expansion of Molien series for 16-D extraspecial group 2^{1+2*4}.

1, 1, 51, 219, 2244, 12815, 69615, 303165, 1180395, 4052070, 12706650, 36580770, 98256600, 247786866, 592040266, 1347148374, 2936245389, 6154632399, 12456241445, 24415459445, 46484089740, 86164059465, 155843612865, 275546946795, 477079706295, 810057618396

Offset

0,3

Comments

The first formula intersperses the terms with zeros, the second formula does not. - Colin Barker, Apr 01 2015

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (8, -20, -8, 126, -168, -196, 680, -239, -1072, 1240, 560, -1820, 560, 1240, -1072, -239, 680, -196, -168, 126, -8, -20, 8, -1).

Formula

G.f.: (1 -7*x^2 +63*x^4 -161*x^6 +1394*x^8 -307*x^10 +7665*x^12 +987*x^14 +13498*x^16 +987*x^18 +7665*x^20 -307*x^22 +1394*x^24 -161*x^26 +63*x^28 -7*x^30 +x^32)/( (1-x)^8*(1+x)^8*(1-x^2)^8*(1+x^2)^8 ), even terms only.

G.f.: (1 -7*x +63*x^2 -161*x^3 +1394*x^4 -307*x^5 +7665*x^6 +987*x^7 +13498*x^8 +987*x^9 +7665*x^10 -307*x^11 +1394*x^12 -161*x^13 +63*x^14 -7*x^15 +x^16)/( (1-x)^8*(1-x^2)^8 ). - Colin Barker, Apr 01 2015

Example

1 + l^2 + 51*l^4 + 219*l^6 + 2244*l^8 + 12815*l^10 + ...

Maple

f(x):=(1 -7*x +63*x^2 -161*x^3 +1394*x^4 -307*x^5 +7665*x^6 +987*x^7 +13498*x^8 +987*x^9 +7665*x^10 -307*x^11 +1394*x^12 -161*x^13 +63*x^14 -7*x^15 +x^16)/( (1-x)^8*(1-x^2)^8 ); seq(coeff(series(f(x), x, n+1), x, n), n = 0..30); # G. C. Greubel, Feb 01 2020

Mathematica

CoefficientList[Series[(1 -7*x +63*x^2 -161*x^3 +1394*x^4 -307*x^5 +7665*x^6 +987*x^7 +13498*x^8 +987*x^9 +7665*x^10 -307*x^11 +1394*x^12 -161*x^13 +63*x^14 -7*x^15 +x^16)/( (1-x)^8*(1-x^2)^8 ), {x, 0, 30}], x] (* G. C. Greubel, Feb 01 2020 *)
LinearRecurrence[{8, -20, -8, 126, -168, -196, 680, -239, -1072, 1240, 560, -1820, 560, 1240, -1072, -239, 680, -196, -168, 126, -8, -20, 8, -1}, {1, 1, 51, 219, 2244, 12815, 69615, 303165, 1180395, 4052070, 12706650, 36580770, 98256600, 247786866, 592040266, 1347148374, 2936245389, 6154632399, 12456241445, 24415459445, 46484089740, 86164059465, 155843612865, 275546946795}, 30] (* Harvey P. Dale, Aug 20 2022 *)

Prog

(PARI) Vec((1-7*x+63*x^2-161*x^3+1394*x^4-307*x^5+7665*x^6+987*x^7+13498*x^8 +987*x^9+7665*x^10-307*x^11+1394*x^12-161*x^13+63*x^14-7*x^15+x^16)/((1-x)^8 *(1-x^2)^8) + O(x^30)) \\ Colin Barker, Apr 01 2015
(Sage)
def f(x): return (1-7*x+63*x^2-161*x^3+1394*x^4-307*x^5+7665*x^6+987*x^7 +13498*x^8+987*x^9+7665*x^10-307*x^11+1394*x^12-161*x^13+63*x^14-7*x^15 +x^16)/((1-x)^8 *(1-x^2)^8)
[( f(x) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Feb 01 2020

Crossrefs

Cf. A014095, A030533, A030536, A030537.

Sequence in context: A007264 A158640 A107253 * A201813 A193250 A204717

Adjacent sequences: A030532 A030533 A030534 * A030536 A030537 A030538

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved