A228866 G.f.: A(x) = 1 + x*B(x), where B(x) = 1 + x^2*C(x)^2, C(x) = 1 + x^3*D(x)^3, D(x) = 1 + x^4*E(x)^4, ...

1, 1, 0, 1, 0, 0, 2, 0, 0, 1, 6, 0, 0, 6, 6, 24, 0, 15, 26, 48, 36, 140, 120, 60, 288, 279, 600, 660, 1476, 822, 2166, 2880, 5100, 7047, 6300, 14100, 21440, 30210, 30054, 62496, 72060, 123180, 174780, 253980, 319488, 497544, 730560, 976020, 1654856, 1997706, 3085932, 4160740, 6426480

Offset: 0

Author

Paul D. Hanna, Sep 06 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^3 + 2*x^6 + x^9 + 6*x^10 + 6*x^13 + 6*x^14 + 24*x^15 +...
where A(x) = 1 + x*B(x),
B(x) = 1 + x^2 + 2*x^5 + x^8 + 6*x^9 + 6*x^12 + 6*x^13 + 24*x^14 +...
B(x) = 1 + x^2*C(x)^2,
C(x) = 1 + x^3 + 3*x^7 + 3*x^11 + 12*x^12 + x^15 + 24*x^16 + 18*x^17 +...
C(x) = 1 + x^3*D(x)^3,
D(x) = 1 + x^4 + 4*x^9 + 6*x^14 + 20*x^15 + 4*x^19 + 60*x^20 + 40*x^21 +...
D(x) = 1 + x^4*E(x)^4,
E(x) = 1 + x^5 + 5*x^11 + 10*x^17 + 30*x^18 + 10*x^23 + 120*x^24 + 75*x^25 +...
E(x) = 1 + x^5*F(x)^5,
F(x) = 1 + x^6 + 6*x^13 + 15*x^20 + 42*x^21 + 20*x^27 + 210*x^28 + 126*x^29 +...
F(x) = 1 + x^6*G(x)^6,
G(x) = 1 + x^7 + 7*x^15 + 21*x^23 + 56*x^24 + 35*x^31 + 336*x^32 + 196*x^33 +...
G(x) = 1 + x^7*H(x)^7,
H(x) = 1 + x^8 + 8*x^17 + 28*x^26 + 72*x^27 + 56*x^35 + 504*x^36 + 288*x^37 +...
...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A108643, A095793.

Programs

PARI

{a(n)=local(A=1);for(k=1,n,A = 1 + (x*A)^(n-k+1) +x*O(x^n));polcoeff(A,n)}
for(n=0,120,print1(a(n),", "))