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A118934
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E.g.f.: exp(x + x^4/4).
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4
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1, 1, 1, 1, 7, 31, 91, 211, 1681, 12097, 57961, 209881, 1874071, 17842111, 117303187, 575683291, 5691897121, 65641390081, 544238393041, 3362783785777, 36455473647271, 485442581801311, 4828464958268491, 35900587138847971
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OFFSET
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0,5
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COMMENTS
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Equals row sums of triangle A118933.
These are the telephone numbers T^(4)_n of [Artioli et al., p. 7]. - Eric M. Schmidt, Oct 12 2017
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LINKS
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FORMULA
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a(n) = a(n-1) + (n-1)*(n-2)*(n-3)*a(n-4) for n>=4, with a(0)=a(1)=a(2)=a(3)=1.
a(n) = Sum_{k=0..floor(n/4)} n!/(4^k*k!*(n-4*k)!). - G. C. Greubel, Mar 07 2021
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[x+x^4/4], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Jan 26 2013 *)
Table[Sum[n!/(4^k*k!*(n-4*k)!), {k, 0, n/4}], {n, 0, 30}]
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PROG
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(PARI) a(n)=if(n<0, 0, if(n==0, 1, a(n-1) + (n-1)*(n-2)*(n-3)*a(n-4)))
(Sage) f=factorial; [sum(f(n)/(4^j*f(j)*f(n-4*j)) for j in (0..n/4)) for n in (0..30)] # G. C. Greubel, Mar 07 2021
(Magma) F:=Factorial; [(&+[F(n)/(4^j*F(j)*F(n-4*j)): j in [0..Floor(n/4)]]): n in [0..30]]; // G. C. Greubel, Mar 07 2021
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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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