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A027638
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Order of 2^n X 2^n unitary group H_n acting on Siegel modular forms.
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4
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4, 96, 46080, 371589120, 48514675507200, 101643290713836748800, 3409750224676138896064512000, 1830483982118721406049481526345728000, 15723497752907010191583185709179507111362560000
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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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FORMULA
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a(n) = 2^(n^2 + 2*n + 2) * Product_{j=1..n} (4^j - 1).
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MAPLE
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seq( 2^(n^2+2*n+2)*product(4^i -1, i=1..n), n=0..12);
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MATHEMATICA
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Table[2^(n^2+2n+2) Product[4^k-1, {k, n}], {n, 0, 10}] (* Harvey P. Dale, May 21 2018 *)
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PROG
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(Magma)
A027638:= func< n | n eq 0 select 4 else 2^(n^2+2*n+2)*(&*[4^j-1: j in [1..n]]) >;
(SageMath)
from sage.combinat.q_analogues import q_pochhammer
def A027638(n): return (-1)^n*2^(n^2 + 2*n + 2)*q_pochhammer(n, 4, 4)
(PARI) a(n) = my(ret=1); for(i=1, n, ret = ret<<(2*i)-ret); ret << (n^2+2*n+2); \\ Kevin Ryde, Aug 13 2022
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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