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A030533 Expansion of Molien series for 4-D extraspecial group 2^{1+2*2}. 5
1, 1, 5, 6, 15, 19, 35, 44, 69, 85, 121, 146, 195, 231, 295, 344, 425, 489, 589, 670, 791, 891, 1035, 1156, 1325, 1469, 1665, 1834, 2059, 2255, 2511, 2736, 3025, 3281, 3605, 3894, 4255, 4579, 4979, 5340, 5781, 6181, 6665, 7106, 7635 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for Molien series.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

FORMULA

G.f.: (x^8-x^6+2*x^4-x^2+1)/(1+x^2)^2/(-1+x^2)^2/(1+x)^2/(-1+x)^2 (not simplified).

G.f.: (x^2-x+1)*(x^2+1) / ((x-1)^4*(x+1)^2). [Colin Barker, Jan 31 2013]

a(n) = n*(2*n^2-9*(-1)^n+13)/24. [Bruno Berselli, Jan 31 2013]

EXAMPLE

1+x^2+5*x^4+6*x^6+15*x^8+19*x^10+35*x^12+44*x^14+69*x^16+...

MATHEMATICA

CoefficientList[Series[(x^2 - x + 1) (x^2 + 1)/((x - 1)^4 (x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 19 2013 *)

PROG

(PARI) select(n->n, Vec((x^8-x^6+2*x^4-x^2+1)/(1+x^2)^2/(-1+x^2)^2/(1+x)^2/(-1+x)^2+O(x^99))) \\ Charles R Greathouse IV, Sep 24 2012

(MAGMA) [(n+1)*(2*n^2+4*n+15+9*(-1)^n)/24: n in [0..50]]; // Vincenzo Librandi, Oct 19 2013

CROSSREFS

Cf. A014095, A030535, A030536, A030537.

Sequence in context: A160109 A191213 A121847 * A227066 A115908 A247962

Adjacent sequences:  A030530 A030531 A030532 * A030534 A030535 A030536

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 17 13:57 EDT 2019. Contains 328113 sequences. (Running on oeis4.)