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 A094717 a(n) = n!*Sum_(i+2j+3k=n, 0<=i<=n, 0<=j<=n, 0<=k<=n, 1/i!/(2j)!/(3k)!). 2
 1, 1, 2, 5, 12, 36, 113, 351, 1080, 3281, 9882, 29646, 88817, 266085, 797526, 2391485, 7173360, 21520080, 64563521, 193700403, 581120892, 1743392201, 5230206126, 15690618378, 47071766561, 141215033961, 423644570442, 1270932914165 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA Limit n -> infty a(n)/3^n = 1/6. E.g.f.: exp(z)*cosh(z)*(exp(z)+2*exp(-z/2)*cos(z*sqrt(3/4)))/3. - Peter Luschny, Jul 11 2012 Empirical G.f.: -(2*x^5-2*x^4+5*x^3-8*x^2+5*x-1) / ((x-1)*(3*x-1)*(x^2+x+1)*(3*x^2-3*x+1)). - Colin Barker, Dec 24 2012 MAPLE A094717_list := proc(n) local i; exp(z)*cosh(z)*(exp(z)+2*exp(-z/2)* cos(z*sqrt(3/4)))/3; series(%, z, n+2); seq(simplify(i!*coeff(%, z, i)), i=0..n) end: A094717_list(27); # Peter Luschny, Jul 11 2012 MATHEMATICA a[n_] := n! Sum[Boole[i + 2j + 3k == n]/(i! (2j)! (3k)!), {i, 0, n}, {j, 0, n}, {k, 0, n}]; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Jul 06 2019 *) PROG (PARI) a(n)=sum(i=0, n, sum(j=0, n, sum(k=0, n, if(n-i-2*j-3*k, 0, n!/(i)!/(2*j)!/(3*k)!)))) CROSSREFS Cf. A024493, A094715. Sequence in context: A303204 A032203 A197444 * A323933 A038142 A287427 Adjacent sequences:  A094714 A094715 A094716 * A094718 A094719 A094720 KEYWORD nonn AUTHOR Benoit Cloitre, May 23 2004 STATUS approved

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Last modified October 19 21:28 EDT 2019. Contains 328244 sequences. (Running on oeis4.)