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A340937 E.g.f.: Sum_{n>=0} log(1+x)^n * (1-x)^(2^n) / n!, an even function. 0
1, -4, 60, -4560, 1617840, -2466858240, 15838238465280, -426053221479325440, 47729463719523621235200, -22079835636445226386614067200, 41831531171322058973799471506227200, -322446010409733312802241919462976450560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..11.

FORMULA

E.g.f.: Sum_{n>=0} log(1+x)^n * (1-x)^(2^n) / n!.

E.g.f.: Sum_{n>=0} log(1-x)^n * (1+x)^(2^n) / n!.

EXAMPLE

E.g.f: A(x) = 1 - 4*x^2/2! + 60*x^4/4! - 4560*x^6/6! + 1617840*x^8/8! - 2466858240*x^10/10! + 15838238465280*x^12/12! + ...

where

A(x) = (1-x) + log(1+x)*(1-x)^2 + log(1+x)^2*(1-x)^4/2! + log(1+x)^3*(1-x)^8/3! + log(1+x)^4*(1-x)^16/4! + ...

also

A(x) = (1+x) + log(1-x)*(1+x)^2 + log(1-x)^2*(1+x)^4/2! + log(1-x)^3*(1+x)^8/3! + log(1-x)^4*(1+x)^16/4! + ...

RELATED SERIES.

arccos(A(x)) = 4*x/2 - 44*x^3/(2^3*3!) + 8836*x^5/(2^5*5!) - 10920780*x^7/(2^7*7!) + 58866344964*x^9/(2^9*9!) - 1318980481299180*x^11/(2^11*11!) + ...

PROG

(PARI) {a(n) = my(A = sum(m=0, 2*n, log(1+x +O(x^(2*n+1)))^m/m! * (1-x +O(x^(2*n+1)))^(2^m) ) ); (2*n)!*polcoeff(A, 2*n)}

for(n=0, 15, print1(a(n), ", "))

CROSSREFS

Sequence in context: A229771 A341275 A338550 * A136385 A173607 A071582

Adjacent sequences:  A340934 A340935 A340936 * A340938 A340939 A340940

KEYWORD

sign

AUTHOR

Paul D. Hanna, Feb 01 2021

STATUS

approved

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Last modified August 4 16:25 EDT 2021. Contains 346447 sequences. (Running on oeis4.)