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A113871
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G.f.: 1/(Sum_{k>=0} (k!)^2 x^k).
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6
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1, -1, -3, -29, -499, -13101, -486131, -24266797, -1571357619, -128264296301, -12894743113075, -1566235727656365, -226180775756251955, -38308065207361046509, -7521255169156107737331, -1694604321825062440852013, -434302821056087233474158259
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: 2/Q(0), where Q(k) = 1 + 1/(1 - (k+1)^2*x/((k+1)^2*x + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 17 2013
a(n) ~ -n!^2 * (1 - 2/n^2 - 5/n^4 - 10/n^5 - 67/n^6 - 332/n^7 - 2152/n^8 - 14946/n^9 - 115583/n^10). - Vaclav Kotesovec, Jul 28 2015
a(0) = 1, a(n) = -Sum_{k=0..n-1} a(k) * ((n-k)!)^2. - Daniel Suteu, Feb 23 2018
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MATHEMATICA
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nn = 20; CoefficientList[Series[1/Sum[(k!)^2 x^k, {k, 0, nn}], {x, 0, nn}], x] (* T. D. Noe, Jan 03 2013 *)
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PROG
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(Sage)
h = 1/(1+x*hypergeometric((1, 2, 2), (), x))
(Sage)
R, C = [1], [1]+[0]*(len-1)
for n in (1..len-1):
for k in range(n, -1, -1):
C[k] = C[k-1] * k^2
C[0] = -sum(C[k] for k in (1..n))
R.append(C[0])
return R
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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