A063030 Reversion of y - y^2 - y^4 + y^5.
0, 1, 1, 2, 6, 19, 63, 220, 795, 2942, 11099, 42536, 165126, 647955, 2565946, 10241616, 41158598, 166402323, 676338003, 2761988994, 11327162406, 46631572295, 192638451780, 798316442580, 3317866307145, 13825837134096
Offset: 0
Links
Programs
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Mathematica
CoefficientList[InverseSeries[Series[y - y^2 - y^4 + y^5, {y, 0, 30}], x], x] -
PARI
a(n)=if(n<1,0,polcoeff(serreverse(x-x^2-x^4+x^5+x*O(x^n)),n))
Formula
D-finite with recurrence 1458*n*(n-1)*(n-2)*(2*n-1) *(981649511*n -2631216939)*a(n) -486*(n-1)*(n-2) *(24210415932*n^3 -114067288649*n^2 +155533650884*n -64732315335)*a(n-1) +54*(n-2) *(39787015892*n^4 -313539301751*n^3 +992577496688*n^2 -1613867842189*n +1173502139880)*a(n-2) +(-27607572942679*n^5 +295135536608825*n^4 -1205223186688595*n^3 +2314131935158975*n^2 -2033367943220766*n +619177732684560)*a(n-3) -5*(5*n-21) *(5408009*n +1144402484)*(5*n-19) *(5*n-18)*(5*n-17) *a(n-4)=0. - R. J. Mathar, Mar 21 2022
a(n+1) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,n) * binomial(2*n-3*k,n). - Seiichi Manyama, Sep 26 2023