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
Simon Burton, Elijah Durso-Sabina, and Natalie C. Brown, Genons, Double Covers and Fault-tolerant Clifford Gates, arXiv:2406.09951 [quant-ph], 2024. See p. 18.
B. Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996), 175-204.
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
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved