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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 EXTENSIONS More terms from Herman P. Robinson. More terms from Ruperto Corso, Dec 14 2011 STATUS approved

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Last modified August 9 01:38 EDT 2022. Contains 356016 sequences. (Running on oeis4.)