A194972 a(n) equals the coefficient of x^n in the (2*n-1)-th iteration of x+x^2 for n>=1.
1, 3, 20, 231, 3864, 85140, 2332616, 76485227, 2921536088, 127421864328, 6248486040840, 340321635330534, 20383240346962440, 1331538898625750100, 94216429100347571448, 7178425650032302557691, 585936966156456139931584, 51011156414845408925712816
Offset: 1
Keywords
Examples
The coefficients of x^k, k>=1, in the odd iterations of x+x^2 begin: n=1: [(1), 1]; n=3: [1,(3), 6, 9, 10, 8, 4, 1]; n=5: [1, 5,(20), 70, 220, 630, 1656, 4014, 8994, 18654, ...]; n=7: [1, 7, 42,(231), 1190, 5810, 27076, 121023, 520626, ...]; n=9: [1, 9, 72, 540,(3864), 26628, 177744, 1153740, 7303164, ...]; n=11:[1, 11, 110, 1045, 9570,(85140), 739332, 6286797, ...]; n=13:[1, 13, 156, 1794, 20020, 218218,(2332616), 24519066, ...]; n=15:[1, 15, 210, 2835, 37310, 481390, 6110468,(76485227), ...]; ... coefficients in parenthesis form the initial terms of this sequence.
Programs
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PARI
{a(n)=local(A=x,G=x+x^2); for(i=1,2*n-1, A=subst(G, x, A+x*O(x^n))); polcoeff(A,n)}