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A221098 E.g.f. satisfies: A(x) = Sum_{n>=0} log(1 + x*A(x)^(4*n))^n/n!. 3
1, 1, 8, 156, 5184, 243280, 14742240, 1097403552, 97012667136, 9936480419424, 1157549828855040, 151193318253405120, 21890302973632558080, 3480525852596442818688, 603034041051994953483264, 113109668528001746742489600, 22839699845167989485088522240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

E.g.f. also satisfies:

(1) A(x) = Sum_{n>=0} binomial(A(x)^(4*n), n) * x^n.

(2) A(x) = Sum_{n>=0} x^n * Sum_{k=0..n} Stirling1(n,k) * A(x)^(4*n*k)/n!.

EXAMPLE

E.g.f.: A(x) = 1 + x + 8*x^2/2! + 156*x^3/3! + 5184*x^4/4! + 243280*x^5/5! +...

where A(x) satisfies:

A(x) = 1 + log(1 + x*A(x)^4) + log(1 + x*A(x)^8)^2/2! + log(1 + x*A(x)^12)^3/3! +...

The e.g.f. also satisfies:

A(x) = 1 + A(x)^4*x + A(x)^8*(A(x)^8-1)*x^2/2! + A(x)^12*(A(x)^12-1)*(A(x)^12-2)*x^3/3! + A(x)^16*(A(x)^16-1)*(A(x)^16-2)*(A(x)^16-3)*x^4/4! +...+ binomial(A(x)^(4*n), n)*x^n +...

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, log(1+x*(A+x*O(x^n))^(4*m))^m/m!)); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, binomial((A+x*O(x^n))^(4*m), m)*x^m)); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

(PARI) {Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}

{a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, sum(k=0, m, Stirling1(m, k)*(A+x*O(x^n))^(4*m*k))*x^m/m!)); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A189981, A221096, A221097, A221099.

Sequence in context: A113668 A120348 A251586 * A171211 A211043 A025605

Adjacent sequences: A221095 A221096 A221097 * A221099 A221100 A221101

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 01 2013

STATUS

approved

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Last modified December 1 21:09 EST 2022. Contains 358484 sequences. (Running on oeis4.)