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

1,2

Links

Table of n, a(n) for n=1..18.

Example

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.

Prog

(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)}

Crossrefs

Cf. A194971, A122888, A112317.

Sequence in context: A058477 A119758 A108527 * A294603 A240957 A335871

Adjacent sequences: A194969 A194970 A194971 * A194973 A194974 A194975

Keyword

nonn

Author

Paul D. Hanna, Sep 06 2011

Status

approved