A063021 Reversion of y - y^2 - y^5.
0, 1, 1, 2, 5, 15, 49, 168, 594, 2150, 7931, 29718, 112814, 432957, 1677050, 6547856, 25742454, 101819100, 404885630, 1617725010, 6491294600, 26147434885, 105691660110, 428578242900, 1742925259725, 7106942278683, 29050303230234, 119014903102956, 488610373729868
Offset: 0
Links
- Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012.
- Index entries for reversions of series
Programs
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Maple
A063021 := proc(n) add(binomial(n-1-3*j,j)*binomial(2*n-3*j-2,n-1)/n,j=0..(n-1)/3) ; end proc: seq(A063021(n),n=0..60) ; # R. J. Mathar, Jul 23 2023
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Mathematica
CoefficientList[InverseSeries[Series[y - y^2 - y^5, {y, 0, 30}], x], x] -
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 */
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PARI
Vec(serreverse(x-x^2-x^5+O(x^66))) /* Joerg Arndt, May 24 2011 */
Formula
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
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