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A197772 G.f.: A(x) = 1/(1 - x*B(x)), where B(x) = 1/(1 - x*C(x)^2); C(x) = 1/(1 - x*D(x)^3); D(x) = 1/(1 - x*E(x)^4); ... 0
1, 1, 2, 6, 25, 138, 968, 8313, 84735, 1000322, 13418848, 201526744, 3348677251, 60981586323, 1207531891440, 25829355773719, 593485342700358, 14577731251921826, 381175458103542506, 10570762449548976706, 309889778765890035970, 9575316933047901325098 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 25*x^4 + 138*x^5 + 968*x^6 +...

The g.f. A = A(x) is generated by:

A = 1/(1-x*B), B = 1/(1-x*C^2), C = 1/(1-x*D^3), D = 1/(1-x*E^4), E = 1/(1-x*F^5), ...

where the coefficients in the respective power series begin:

B: [1, 1, 3, 14, 87, 672, 6202, 66622, 817205, 11278833, ...];

C: [1, 1, 4, 25, 203, 1989, 22627, 291964, 4206530, 66905338, ...];

D: [1, 1, 5, 39, 389, 4600, 62087, 935506, 15512217, 280252770, ...];

E: [1, 1, 6, 56, 661, 9141, 142642, 2458133, 46147009, 935047405, ...];

F: [1, 1, 7, 76, 1035, 16373, 289864, 5622842, 117940453, 2651283277, ...]; ...

and the coefficients in the indicated powers begin:

C^2: [1, 2, 9, 58, 472, 4584, 51481, 655244, 9318663, ...];

D^3: [1, 3, 18, 148, 1491, 17496, 232556, 3441024, 56009937, ...];

E^4: [1, 4, 30, 300, 3605, 49656, 763968, 12920820, 237676330, ...];

F^5: [1, 5, 45, 530, 7400, 117096, 2048865, 39048150, 802555995, ...]; ...

PROG

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

CROSSREFS

Cf. A121587.

Sequence in context: A128230 A084784 A255841 * A135881 A007815 A195259

Adjacent sequences:  A197769 A197770 A197771 * A197773 A197774 A197775

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 09 2011

STATUS

approved

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Last modified August 9 03:22 EDT 2022. Contains 356016 sequences. (Running on oeis4.)