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 A027629 Molien series for complex 8-dimensional group N_3 of order 2^(2.3+2), a central extension of an extraspecial 2-group. 3
 1, 15, 135, 870, 3993, 14157, 41535, 105740, 241281, 504811, 984423, 1811250, 3173625, 5334057, 8649279, 13593624, 20785985, 31020615, 45302023, 64884222, 91314585, 126482565, 172673535, 232628004, 309606465, 407460131, 530707815, 684619210, 875304825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 B. Runge, On Siegel modular forms II, Nagoya Math. J., 138 (1995), 179-197. Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1). FORMULA G.f.: (1 + 7*x + 43*x^2 + 154*x^3 + 43*x^4 + 7*x^5 + x^6)/(1-x)^8. From Colin Barker, Jan 03 2017: (Start) a(n) = (630 + 2376*n + 2891*n^2 + 1673*n^3 + 980*n^4 + 644*n^5 + 224*n^6 + 32*n^7) / 630. a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7. (End) E.g.f.: (630 +8820*x +33390*x^2 +53445*x^3 +33180*x^4 +8484*x^5 +896*x^6 +32*x^7)*exp(x)/630. - G. C. Greubel, Feb 01 2020 MAPLE seq( (1+n)*(1+2*n)*(3+2*n)*(210 +22*n +43*n^2 +32*n^3 +8*n^4)/630, n=0..30); # G. C. Greubel, Feb 01 2020 MATHEMATICA Table[(1+n)*(1+2*n)*(3+2*n)*(210 +22*n +43*n^2 +32*n^3 +8*n^4)/630, {n, 0, 30}] (* G. C. Greubel, Feb 01 2020 *) PROG (PARI) Vec((1+7*x+43*x^2+154*x^3+43*x^4+7*x^5+x^6) / (1-x)^8 + O(x^30)) \\ Colin Barker, Jan 03 2017 (MAGMA) [(1+n)*(1+2*n)*(3+2*n)*(210 +22*n +43*n^2 +32*n^3 +8*n^4)/630: n in [0..30]]; // G. C. Greubel, Feb 01 2020 (Sage) [(1+n)*(1+2*n)*(3+2*n)*(210 +22*n +43*n^2 +32*n^3 +8*n^4)/630 for n in (0..30)] # G. C. Greubel, Feb 01 2020 (GAP) List([0..30], n-> (1+n)*(1+2*n)*(3+2*n)*(210 +22*n +43*n^2 +32*n^3 +8*n^4)/630); # G. C. Greubel, Feb 01 2020 CROSSREFS Cf. A027628, A027630. Sequence in context: A230659 A228583 A027630 * A023013 A036217 A022643 Adjacent sequences:  A027626 A027627 A027628 * A027630 A027631 A027632 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 1 16:29 EST 2021. Contains 349430 sequences. (Running on oeis4.)