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Search: id:A123853
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| A123853 |
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Numerators in asymptotic expansion of cubic recurrence sequence A123851. |
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+0
7
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| 1, 3, -15, 113, -5397, 84813, -3267755, 74391561, -15633072909, 465681118929, -31041303829713, 1145088996404679, -185348722911971841, 8165727090278785521, -778296382754673737187, 39898888480559205453945, -35033447016186321707305533
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A cubic analog of the asymptotic expansion A116603 of Somos's quadratic recurrence sequence A052129. Denominators are A123854.
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003, p. 446.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl. (to appear).
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LINKS
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J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant
Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant
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EXAMPLE
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A123851(n) ~ c^(3^n)*n^(- 1/2)/(1 + 3/4n - 15/32n^2 + 113/128n^3 - 5397/2048n^4 + ...) where c = 1.1563626843322... is the cubic recurrence constant A123852.
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MAPLE
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f:=proc(t, x) exp(sum(ln(1+m*x)/t^m, m=1..infinity)); end; for j from 0 to 29 do numer(coeff(series(f(3, x), x=0, 30), x, j)); od;
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PROGRAM
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(PARI) {a(n) = local(A); if(n < 0, 0, A = 1 + O(x) ; for( k = 1, n, A = truncate(A) + x * O(x^k); A += x^k * polcoeff( 3/4 * (subst(1/A, x, x^2/(1-x^2))^2/(1-x^2) - 1/subst(A, x, x^2)^(2/3)), 2*k ) ); numerator( polcoeff( A, n ) ) ) } /* Michael Somos Aug 23 2007 */
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CROSSREFS
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Cf. A052129, A112302, A116603, A123851, A123852, A123854.
Sequence in context: A058104 A056053 A059849 this_sequence A166885 A082163 A074596
Adjacent sequences: A123850 A123851 A123852 this_sequence A123854 A123855 A123856
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KEYWORD
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frac,sign
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AUTHOR
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Petros Hadjicostas and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Oct 15 2006
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