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A242240
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Expansion of Jacobi sn(x, 1/2) / cd(x, 1/2).
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2
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0, 1, 0, 0, 0, 12, 0, 0, 0, 3024, 0, 0, 0, 4390848, 0, 0, 0, 21224560896, 0, 0, 0, 257991277243392, 0, 0, 0, 6628234834692624384, 0, 0, 0, 319729080846260095008768, 0, 0, 0, 26571747463798134334265819136, 0, 0, 0, 3564202847752289659513902717468672, 0, 0, 0
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OFFSET
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0,6
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LINKS
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FORMULA
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E.g.f.: sn(x, 1/2) / cd(x, 1/2).
E.g.f. A(x) satisfies A(x)^2 = sinh(2 * Integral A(x) dx). - Michael Somos, Jun 17 2017
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EXAMPLE
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G.f. = x + 12*x^5 + 3024*x^9 + 4390848*x^13 + 21224560896*x^17 + ...
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MATHEMATICA
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a[ n_] := If[ n<0, 0, n! SeriesCoefficient[ JacobiSN[x, 1/2] / JacobiCD[x, 1/2], {x, 0, n}]];
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PROG
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(PARI) {a(n) = if( n<0, 0, n! * polcoeff( serreverse( intformal( (1 + x^4 + x * O(x^n))^(-1/2))), n))};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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