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 A027639 Order of unitary 2^n X 2^n group H_{n,4} acting on Siegel modular forms. 2
 4, 32, 3072, 2752512, 21139292160, 1342091380654080, 692647993190048071680, 2882479558988139892026900480, 96342151992701835341576224427212800, 25811138467998276182105365247324712232550400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 57-85. LINKS G. C. Greubel, Table of n, a(n) for n = 0..45 B. Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996), 175-204. FORMULA a(n) = 2^(n^2 + 2*n + 2) * Product_{j=1..n} (2^j - 1). a(n) = (-1)^n * 2^(n^2 + 2*n + 2) * (2, 2)_{n}, where (q, q)_{n} is the q-Pochhammer symbol. - G. C. Greubel, Aug 04 2022 MAPLE seq(2^(n^2+2*n+2)*mul(2^i-1, i=1..n), n=0..10); MATHEMATICA a[n_]:= (-1)^n*2^(n^2 +2*n+2)*QPochhammer[2, 2, n]; Table[a[n], {n, 0, 15}] (* G. C. Greubel, Aug 04 2022 *) PROG (Magma) A027639:= func< n | n eq 0 select 4 else 2^(n^2+2*n+2)*(&*[2^j-1: j in [1..n]]) >; [A027639(n): n in [0..15]]; // G. C. Greubel, Aug 04 2022 (SageMath) from sage.combinat.q_analogues import q_pochhammer def A027639(n): return (-1)^n*2^(n^2 + 2*n + 2)*q_pochhammer(n, 2, 2) [A027639(n) for n in (0..15)] # G. C. Greubel, Aug 04 2022 (PARI) a(n) = my(ret=1); for(i=1, n, ret = ret<

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Last modified March 25 06:19 EDT 2023. Contains 361511 sequences. (Running on oeis4.)