A027638 Order of 2^n X 2^n unitary group H_n acting on Siegel modular forms.

4, 96, 46080, 371589120, 48514675507200, 101643290713836748800, 3409750224676138896064512000, 1830483982118721406049481526345728000, 15723497752907010191583185709179507111362560000

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..39

B. Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996), 175-204.

Index entries for sequences related to modular groups

Formula

a(n) = A003956(n)/2.

a(n) = 2^(n^2 + 2*n + 2) * Product_{j=1..n} (4^j - 1).

Maple

seq( 2^(n^2+2*n+2)*product(4^i -1, i=1..n), n=0..12);

Mathematica

Table[2^(n^2+2n+2) Product[4^k-1, {k, n}], {n, 0, 10}] (* Harvey P. Dale, May 21 2018 *)

Prog

(Magma)
A027638:= func< n | n eq 0 select 4 else 2^(n^2+2*n+2)*(&*[4^j-1: j in [1..n]]) >;
[A027638(n): n in [0..15]]; // G. C. Greubel, Aug 04 2022
(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)
[A027638(n) for n in (0..15)] # G. C. Greubel, Aug 04 2022
(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

Crossrefs

Cf. A003956, A027672, A027639.

Sequence in context: A307934 A059201 A323818 * A309483 A333539 A356808

Adjacent sequences: A027635 A027636 A027637 * A027639 A027640 A027641

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved