cp's OEIS Frontend

A063021 Reversion of y - y^2 - y^5.

%I A063021 #36 Nov 09 2024 10:03:58
%S A063021 0,1,1,2,5,15,49,168,594,2150,7931,29718,112814,432957,1677050,
%T A063021 6547856,25742454,101819100,404885630,1617725010,6491294600,
%U A063021 26147434885,105691660110,428578242900,1742925259725,7106942278683,29050303230234,119014903102956,488610373729868
%N A063021 Reversion of y - y^2 - y^5.
%H A063021 Vladimir Kruchinin, <a href="http://arxiv.org/abs/1211.3244">The method for obtaining expressions for coefficients of reverse generating functions</a>, arXiv:1211.3244 [math.CO], 2012.
%H A063021 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A063021 a(n) = Sum_{j=0..(n-1)/3} C(n-1-3*j,j)*C(2*n-3*j-2,n-1)/n, n>0, a(0)=0. - _Vladimir Kruchinin_, May 24 2011
%F A063021 D-finite with recurrence +18378869*n*(n-1)*(n-2)*(n-3)*a(n) -2*(n-1)*(n-2)*(n-3)*(45648297*n -34126858)*a(n-1) +10*(n-2)*(n-3)*(2024320*n^2 +38560275*n -118224988)*a(n-2) +1500*(n-3)*(133915*n^3 -1577680*n^2 +6193631*n -8109122)*a(n-3) +5*(-52401875*n^4 +711510000*n^3 -3716005375*n^2 +8966267250*n -8515940832)*a(n-4) -250*(5*n-26)*(173375*n^3 -2045825*n^2 +7891985*n -9883503)*a(n-5) +131250*(5*n-27)*(5*n-31) *(5*n-24)*(5*n-28)*a(n-6)=0. - _R. J. Mathar_, Jul 23 2023
%p A063021 A063021 := proc(n)
%p A063021     add(binomial(n-1-3*j,j)*binomial(2*n-3*j-2,n-1)/n,j=0..(n-1)/3) ;
%p A063021 end proc:
%p A063021 seq(A063021(n),n=0..60) ; # _R. J. Mathar_, Jul 23 2023
%t A063021 CoefficientList[InverseSeries[Series[y - y^2 - y^5, {y, 0, 30}], x], x]
%o A063021 (Maxima) a(n):=sum(binomial(n-1-3*j,j)*binomial(2*n-3*j-2,n-1),j,0,(n-1)/3)/n; /* _Vladimir Kruchinin_, May 24 2011 */
%o A063021 (PARI) Vec(serreverse(x-x^2-x^5+O(x^66))) /* _Joerg Arndt_, May 24 2011 */
%K A063021 nonn,easy
%O A063021 0,4
%A A063021 _Olivier Gérard_, Jul 05 2001