Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
proposed
approved
editing
proposed
a(n) = Sum_{i=1..n}((Sum_{l=0..i}(binomial(i,l)*(Sum_{j=0=(3*(i-l))/7}((-1)^j*binomial(i-l,j)*binomial(-l+3*(-l-2*j+i)-j+i-1,3*(-l-2*j+i)-j)))*(-1)^l))*a(n-i))/n, a(0)=1. - _Vladimir Kruchinin, _, Apr 07 2017
proposed
editing
editing
proposed
a[n_] := a[n] = If[n == 0, 1, Sum[(Sum[Binomial[i, l] (Sum[(-1)^j Binomial[i - l, j] Binomial[-l + 3(-l - 2j + i) - j + i - 1, 3(-l - 2j + i) - j], {j, 0, (3(i - l))/7}]) (-1)^l, {l, 0, i}]) a[n - i], {i, 1, n}]/n];
a /@ Range[1, 23] (* Jean-François Alcover, Sep 24 2019, after Vladimir Kruchinin *)
approved
editing
editing
approved
a(n):=if n=0 then 1 else sum((sum(binomial(i, l)*(sum((-1)^j*binomial(i-l, j)*binomial(-l+3*(-l-2*j+i)-j+i-1, 3*(-l-2*j+i)-j), j, 0, (3*(i-l))/7))*(-1)^l, l, 0, i))*a(n-i), i, 1, n)/n; /* _Vladimir Kruchinin, _, Apr 07 2017 */
proposed
editing
editing
proposed
a(n) = Sum_{i=1..n}((Sum_{l=0..i}(binomial(i,l)*(Sum_{j=0=(3*(i-l))/7}((-1)^j*binomial(i-l,j)*binomial(-l+3*(-l-2*j+i)-j+i-1,3*(-l-2*j+i)-j)))*(-1)^l))*a(n-i))/n, a(0)=1. - Vladimir Kruchinin, Apr 07 2017
(Maxima)
a(n):=if n=0 then 1 else sum((sum(binomial(i, l)*(sum((-1)^j*binomial(i-l, j)*binomial(-l+3*(-l-2*j+i)-j+i-1, 3*(-l-2*j+i)-j), j, 0, (3*(i-l))/7))*(-1)^l, l, 0, i))*a(n-i), i, 1, n)/n; /* Vladimir Kruchinin, Apr 07 2017 */
approved
editing
editing
approved