A300152 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^(n^2) - A(x)^n )^n.

1, 1, 4, 204, 21365, 3655450, 914720443, 314376587287, 142230235674161, 82054323238595173, 58859164893105387442, 51422171965089961951920, 53779967726784762649882252, 66358210285736859276931328215, 95403541500521180624070289201028, 158111431872131942988858401878995245, 299245447906369767603866411915527014775

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Example

G.f.: A(x) = 1 + x + 4*x^2 + 204*x^3 + 21365*x^4 + 3655450*x^5 + 914720443*x^6 + 314376587287*x^7 + 142230235674161*x^8 + 82054323238595173*x^9 + ...
such that
1 = 1 + ((1+x) - A(x)) + ((1+x)^4 - A(x)^2)^2 + ((1+x)^9 - A(x)^3)^3 + ((1+x)^16 - A(x)^4)^4 + ((1+x)^25 - A(x)^5)^5 + ((1+x)^36 - A(x)^6)^6 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = Vec( sum(m=0, #A, ((1+x +x*O(x^#A))^(m^2) - Ser(A)^m)^m ) )[#A] ); A[n+1]}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A304639.

Sequence in context: A317273 A049656 A129465 * A260639 A222282 A087924

Adjacent sequences: A300149 A300150 A300151 * A300153 A300154 A300155

Keyword

nonn

Author

Paul D. Hanna, Jun 30 2018

Status

approved