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A012091
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cos(arcsin(arctan(x)))=1-1/2!*x^2+5/4!*x^4-109/6!*x^6+4521/8!*x^8...
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1
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1, -1, 5, -109, 4521, -330681, 36468717, -5721101541, 1205289090513, -328897528901361, 112769846051251797, -47472161654530776285, 24068680135210975714425, -14466929567049590650593705
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history;
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internal format)
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..13.
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FORMULA
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a(n) = (2*n)!*sum(k=1..2*n, ((2*k)!*binomial(2*k-2,k-1)*(-1)^(n+k+1)*sum(i=2*k..2*n, (2^(i+1)*stirling1(i,2*k)*binomial(2*n-1,i-1))/i!))/(k*2^(4*k))) with n>0, a(0)=1. [Vladimir Kruchinin, Oct 08 2012]
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MATHEMATICA
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With[{nn=30}, Take[CoefficientList[Series[Cos[ArcSin[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Feb 07 2015 *)
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PROG
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(Maxima) a[n]:=if n=0 then 1 else (2*n)!*sum(((2*k)!*binomial(2*k-2, k-1)*(-1)^(n+k+1)*sum((2^(i+1)*stirling1(i, 2*k)*binomial(2*n-1, i-1))/i!, i, 2*k, 2*n))/(k*2^(4*k)), k, 1, 2*n); makelist(a[n], n, 0, 13); [Vladimir Kruchinin, Oct 08 2012]
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CROSSREFS
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Cf. A012254.
Sequence in context: A012121 A014180 A012122 * A322896 A296743 A358781
Adjacent sequences: A012088 A012089 A012090 * A012092 A012093 A012094
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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