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A233861 E.g.f. satisfies: A'(x) = Product_{n>=1} (1 + A(x)^n), where A(0) = 0. 2
1, 1, 3, 21, 171, 1821, 24123, 373941, 6652971, 134043021, 3015804123, 74896835301, 2035155307851, 60060014359101, 1912775342667003, 65386505879278101, 2387952288823631211, 92787780103004673261, 3822149820074294439963, 166370252948982266633541, 7630279185863896475367051 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..110

FORMULA

E.g.f. satisfies: log(A'(x)) = Sum_{n>=1} A000593(n)*A(x)^n/n, where A000593(n) is the sum of odd divisors of n.

Contribution from Paul D. Hanna, Jan 08 2017: (Start)

E.g.f. A(x) satisfies:

(1) A(x) = Series_Reversion( Integral Product_{n>=1} 1/(1+x^n) dx ).

(2) A(x) = Integral Product_{n>=1} (1 + A(x)^n) dx.

(End)

EXAMPLE

E.g.f. A(x) = x + x^2/2! + 3*x^3/3! + 21*x^4/4! + 171*x^5/5! + 1821*x^6/6! +...

where

A'(x) = (1 + A(x)) * (1 + A(x)^2) * (1 + A(x)^3) * (1 + A(x)^4) * (1 + A(x)^5) *...

PROG

(PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(prod(k=1, n, 1+A^k+x*O(x^n)))); n!*polcoeff(A, n)}

for(n=1, 30, print1(a(n), ", "))

CROSSREFS

Cf. A233860.

Sequence in context: A189475 A331328 A206178 * A206397 A247480 A228923

Adjacent sequences:  A233858 A233859 A233860 * A233862 A233863 A233864

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 16 2013

STATUS

approved

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Last modified August 14 13:55 EDT 2020. Contains 336481 sequences. (Running on oeis4.)