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A185618 G.f.: A(x) = 1/(1 - x/((1-x) - x/((1-x)^2 - x/((1-x)^3 -...)))), a continued fraction. 1
1, 1, 3, 12, 57, 306, 1807, 11538, 78739, 569533, 4339187, 34654038, 288981540, 2508261208, 22599555849, 210891194677, 2034166628300, 20245403842599, 207589233294167, 2189866971393096, 23736645165616944, 264066371438676327 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 21 02:02 EDT 2019. Contains 325189 sequences. (Running on oeis4.)