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A027639
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Order of unitary 2^n X 2^n group H_{n,4} acting on Siegel modular forms.
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2
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4, 32, 3072, 2752512, 21139292160, 1342091380654080, 692647993190048071680, 2882479558988139892026900480, 96342151992701835341576224427212800, 25811138467998276182105365247324712232550400
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OFFSET
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0,1
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REFERENCES
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B. Runge, On Siegel modular forms I, J. Reine Angew. Math., 436 (1993), 57-85.
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LINKS
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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.
Index entries for sequences related to modular groups
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FORMULA
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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
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MAPLE
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seq(2^(n^2+2*n+2)*mul(2^i-1, i=1..n), n=0..10);
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MATHEMATICA
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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 *)
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PROG
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(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<<i-ret); ret << (n^2 + 2*n + 2); \\ Kevin Ryde, Aug 13 2022
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CROSSREFS
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Cf. A005329.
Sequence in context: A258122 A012092 A336304 * A117620 A347484 A059904
Adjacent sequences: A027636 A027637 A027638 * A027640 A027641 A027642
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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