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A004130
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Numerators in expansion of (1-x)^{-1/4}.
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4
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1, 1, 5, 15, 195, 663, 4641, 16575, 480675, 1762475, 13042315, 48612265, 729183975, 2748462675, 20809788825, 79077197535, 4823709049635, 18443593425075, 141400882925575, 543277076503525, 8366466978154285, 32270658344309385
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Numerators in expansion of sqrt(1/sqrt(1-4x)). - Paul Barry (pbarry(AT)wit.ie), Jul 12 2005
Denominators are in A088802. - Michael Somos Aug 23 2007
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FORMULA
| a(n) = prod(k=1, n, (4k-3)/k * 2^A007814(k)), proved by Mitch Harris, following a conjecture by R. Stephan.
a(n) = 2^(e_2((2n)!)-n)/n! Product[4k+1,{k,0,n-1}], where e_2((2n)!) is the highest power of 2 that divides (2n)! (sequence A005187). - Emanuele Munarini, Jan 25 2011
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MATHEMATICA
| Table[Numerator[Binomial[-1/4, n] (-1)^n], {n, 0, 20}]
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PROG
| (PARI) {a(n) = if( n<0, 0, numerator( polcoeff( (1 - x +x*O(x^n))^(-1/4), n ) ) ) } /* Michael Somos Aug 23 2007 */
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CROSSREFS
| Cf. A004134.
Cf. A004981, A034255, A034385, A048882.
Cf. A007696, A000265, A049606.
Sequence in context: A174850 A143048 A120602 * A088869 A134715 A053918
Adjacent sequences: A004127 A004128 A004129 * A004131 A004132 A004133
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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