A119685 G.f. satisfies: A(x) = x + A(x^2/(1-x)^2).

1, 1, 2, 4, 8, 17, 38, 88, 208, 497, 1194, 2877, 6948, 16821, 40846, 99539, 243536, 598353, 1476370, 3657883, 9098420, 22713077, 56887062, 142897576, 359879600, 908373713, 2297266554, 5819357841, 14762051140, 37491373173, 95311970590

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Formula

a(1) = 1; a(n) = Sum_{k=1..floor(n/2)} binomial(n-1,2*k-1) * a(k). - Ilya Gutkovskiy, Apr 07 2022

Example

A(x) = x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 38*x^7 + 88*x^8 +...

Prog

(PARI) {a(n)=local(F=x^2/(1-x+x*O(x^n))^2, A=x); if(n<1, 0, for(i=1, #binary(n), A=x+subst(A, x, F)); polcoeff(A, n))}

Crossrefs

Cf. A119262.

Sequence in context: A107597 A082499 A100131 * A025276 A006461 A257300

Adjacent sequences: A119682 A119683 A119684 * A119686 A119687 A119688

Keyword

nonn

Author

Paul D. Hanna, Jun 08 2006

Status

approved