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A233860 E.g.f. satisfies: A'(x) = Product_{n>=1} 1/(1 - A(x)^n), where A(0) = 0. 2
1, 1, 5, 35, 355, 4465, 69125, 1252475, 26151475, 616872025, 16234589525, 471382586675, 14970245087875, 516142537458625, 19199498482905125, 766394702651760875, 32676482018991377875, 1482055899582130035625, 71248344993651091083125, 3618867148116847594611875 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

CONJECTURES.

a(n) == 1 (mod 2).

a(n) == 0 (mod 5^k) for n >= 5*k-2.

a(n) == 0 (mod 7^k) for n >= 7*k.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..380

FORMULA

E.g.f.: Series_Reversion( Integral eta(x) dx ), where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor.

E.g.f. A(x) satisfies: log(A'(x)) = Sum_{n>=1} sigma(n)*A(x)^n/n.

EXAMPLE

E.g.f. A(x) = x + x^2/2! + 5*x^3/3! + 35*x^4/4! + 355*x^5/5! + 4465*x^6/6! +...

where

A'(x) = 1/( (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(1/prod(k=1, n, 1-A^k+x*O(x^n)))); n!*polcoeff(A, n)}

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

(PARI) {a(n)=local(A=serreverse(intformal(eta(x+x*O(x^n))))); n!*polcoeff(A, n)}

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

CROSSREFS

Cf. A233861.

Sequence in context: A113342 A262248 A201367 * A258902 A125864 A210996

Adjacent sequences:  A233857 A233858 A233859 * A233861 A233862 A233863

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 16 2013

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)