A191241 Reversion of x - x^2 - 2*x^5.

1, 1, 2, 5, 16, 56, 204, 759, 2880, 11132, 43732, 174122, 700952, 2847840, 11661592, 48080811, 199433880, 831649380, 3484523460, 14662036550, 61931353880, 262503848400, 1116179957160, 4759795460550, 20351410848288, 87229181620152, 374722175164232, 1613115479264852, 6957700944802160, 30064406772108544

Offset

1,3

Comments

For the reversion of x - a*x^2 - b*x^5 (a!=0, b!=0) we have a(n) = Sum_{j=0..floor((n-1)/3)} a^(n-4*j-1)*b^j*binomial(n-3*j-1,j)*binomial(2*n-3*j-2,n-1)/n, n > 0.

Links

Table of n, a(n) for n=1..30.

Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012.

Formula

a(n) = Sum_{j=0..floor((n-1)/3)} 2^j*binomial(n-3*j-1,j)*binomial(2*n-3*j-2,n-1)/n, n > 0.

Prog

(Maxima)
a(n):=sum(2^j*binomial(n-3*j-1, j)*binomial(2*n-3*j-2, n-1), j, 0, (n-1)/3)/n;

Crossrefs

Sequence in context: A057973 A102461 A176332 * A052708 A149973 A149974

Adjacent sequences: A191238 A191239 A191240 * A191242 A191243 A191244

Keyword

nonn

Author

Vladimir Kruchinin, May 28 2011

Status

approved