A185618 G.f.: A(x) = 1/(1 - x/((1-x) - x/((1-x)^2 - x/((1-x)^3 -...)))), a continued fraction.

1, 1, 3, 12, 57, 306, 1807, 11538, 78739, 569533, 4339187, 34654038, 288981540, 2508261208, 22599555849, 210891194677, 2034166628300, 20245403842599, 207589233294167, 2189866971393096, 23736645165616944, 264066371438676327

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 57*x^4 + 306*x^5 + 1807*x^6 +...
Related functions.
Let A(x) = 1/(1 - x*B(x)), B(x) = 1/((1-x) - x*C(x)),
C(x) = 1/((1-x)^2 - x*D(x)), D(x) = 1/((1-x)^3 - x*E(x)),
E(x) = 1/((1-x)^4 - x*F(x)), F(x) = 1/((1-x)^5 - x*G(x)),
G(x) = 1/((1-x)^6 - x*H(x)), H(x) = 1/((1-x)^7 - x*I(x)), ...
then the coefficients in these functions begin:
B: [1,2,7,32,172,1035,6785,47667,355031,2782507,...];
C: [1,3,12,63,385,2604,19009,147520,1205168,10294340,...];
D: [1,4,18,106,726,5458,43987,374704,3342770,31032313,...];
E: [1,5,25,162,1226,10127,89216,827354,8005125,80319277,...];
F: [1,6,33,232,1917,17227,164430,1647071,17166202,185045995,...];
G: [1,7,42,317,2832,27461,281849,3028595,33790412,389155832,...];
H: [1,8,52,418,4005,41620,456429,5230214,62129311,760630876,...];
I: [1,9,63,536,5471,60584,706113,8584910,108063440,1400175142,...]; ...

Prog

(PARI) {a(n)=local(A=1/(1-x+x*O(x^n))^n); for(k=1, n, A=1/((1-x)^(n-k)-x*A+x*O(x^n))); polcoeff(A, n)}

Crossrefs

Sequence in context: A128326 A323631 A014333 * A027710 A307495 A302101

Adjacent sequences: A185615 A185616 A185617 * A185619 A185620 A185621

Keyword

nonn

Author

Paul D. Hanna, Mar 05 2011

Status

approved