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Search: id:A012244
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| A012244 |
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a[n+2] = (2n+3) a[n+1] + (n+1)^2 a[n]. |
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+0
5
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| 1, 1, 4, 24, 204, 2220, 29520, 463680, 8401680, 172504080, 3958113600, 100370793600, 2787459998400, 84139894238400, 2742857884166400, 96034297911552000, 3594206259195552000, 143193586818810528000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) is the number of n-letter words from an n-letter alphabet such that no letter appears more than twice. - Paul Boddington (psb(AT)maths.warwick.ac.uk), Nov 17 2003
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LINKS
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K. S. Brown, Integer Sequences Related To PI
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FORMULA
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E.g.f. = (1 - 2*x - x^2)^(-1/2). - Paul Boddington (psb(AT)maths.warwick.ac.uk), Nov 17 2003
a(n) = n!/2^n*A006139(n) = n!*Sum_{k=floor(n/2)..n} 2^(k-n)*binomial(n, k)*binomial(k, n-k). Sum_{n>=0} a(n)*x^n/n!^2 = exp(x)*BesselI(0, sqrt(2)*x). a(n) is the central coefficient of n!*(1+x+x^2/2)^n. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 22 2004
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MAPLE
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f := proc(n) option remember; if n <= 1 then 1 else (2*n-1)*f(n-1) +(n-1)^2*f(n-2); fi; end;
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CROSSREFS
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Cf. A089975.
Sequence in context: A136229 A138419 A089946 this_sequence A050388 A010039 A112141
Adjacent sequences: A012241 A012242 A012243 this_sequence A012245 A012246 A012247
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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