A197772 - OEIS

%I #19 Mar 30 2012 18:37:31

%S 1,1,2,6,25,138,968,8313,84735,1000322,13418848,201526744,3348677251,

%T 60981586323,1207531891440,25829355773719,593485342700358,

%U 14577731251921826,381175458103542506,10570762449548976706,309889778765890035970,9575316933047901325098

%N 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); ...

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

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

%e 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), ...

%e where the coefficients in the respective power series begin:

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

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

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

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

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

%e and the coefficients in the indicated powers begin:

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

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

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

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

%o (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)}

%Y Cf. A121587.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 09 2011