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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

M. Lotkin, A set of test matrices, Math. Comp., 9 (1955), 153-161.

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

Ruperto Corso, Table of n, a(n) for n = 1..41

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

Adjacent sequences:  A002201 A002202 A002203 * A002205 A002206 A002207

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Herman P. Robinson.

More terms from Ruperto Corso, Dec 14 2011

STATUS

approved

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Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)