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A002204 An ill-conditioned determinant.
(Formerly M4313 N1806)
1
1, 6, 720, 1512000, 53343360000, 31052236723200000, 295415578275110092800000, 45669605890716810734764032000000, 114309087153174410876339218101043200000000, 4620689394791469131629562883903627872698368000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
M. Lotkin, A set of test matrices, Math. Comp., 9 (1955), 153-161.
FORMULA
Recurrence: a(n) = binomial(2n-2,n-2)*binomial(2n-2,n-1)*(2n-1)*a(n-1) with a(1)=1.
a(n) ~ A^3 * 2^(n*(2*n-1) - 1/12) / (exp(1/4) * Pi^n * n^(3/4)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019
MATHEMATICA
Table[BarnesG[2*n + 1]/(n*BarnesG[n + 1]^4), {n, 1, 10}] (* Vaclav Kotesovec, Feb 24 2019 *)
PROG
(PARI) for(n=1, 100, print1((-1)^(n+1)/matdet(matrix(n, n, i, j, if(i>1, 1/(i+j-1), 1)))", ")) /* Ruperto Corso, Dec 14 2011 */
CROSSREFS
Sequence in context: A188960 A100732 A003923 * A052295 A169668 A168467
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Herman P. Robinson
More terms from Ruperto Corso, Dec 14 2011
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)