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A051029
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Ramanujan's b-series.
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3
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2, 138, 11468, 951690, 78978818, 6554290188, 543927106802, 45139395574362, 3746025905565260, 310875010766342202, 25798879867700837522, 2140996154008403172108, 177676881902829762447458
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The "amazing" identity of Ramanujan is a(n)^3 + b(n)^3 = c(n)^3 + (-1)^n, where a(n)=A051028(n), b(n)=A051029(n) and c(n)=A051030(n). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
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REFERENCES
| M. D. Hirschhorn, A Proof in the Spirit of Zeilberger of an Amazing Identity of Ramanujan.
Jung Hun Han and Michael D. Hirschhorn, Another look at an amazing identity of Ramanujan, Math. Magazine, 79, No. 2, 2006, 302-304.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| G.f.: f(x)=(2-26x-12x^2)/(1-82x-82x^2+x^3).
X(n+1)=AX(n), where X(n)=transpose(A051028(n), A051029(n), A051030(n)) and A = matrix (3,3,[63,104,-68; 64,104,-67; 80,131,-85)]). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
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MAPLE
| g:=(2-26*x-12*x^2)/(1-82*x-82*x^2+x^3): gser:=series(g, x=0, 20): seq(coeff(gser, x, n), n=0..12); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
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CROSSREFS
| Cf. A051028, A051030.
Sequence in context: A195379 A087619 A157072 * A084560 A054681 A152509
Adjacent sequences: A051026 A051027 A051028 * A051030 A051031 A051032
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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