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A195415 E.g.f.: Sum_{n>=1} tanh(n*x)^n = Sum_{n>=1} a(n)*4^(n-1)/n!. 0
1, 2, 10, 92, 1351, 28982, 855100, 33214232, 1642999501, 100843185962, 7520379392890, 669760178257172, 70211429619908851, 8558006664633638942, 1200128210993564085880, 191861070874818576596912, 34685967730611200643509401, 7041037426518318365605795922 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

FORMULA

E.g.f.: Sum_{n>=1} ( 1 - 2/(1+exp(2*n*x)) )^n = Sum_{n>=1} a(n)*4^(n-1)/n!.

EXAMPLE

E.g.f.: A(x) = x + 8*x^2/2! + 160*x^3/3! + 5888*x^4/4! + 345856*x^5/5! +...

or, equivalently,

A(x) = x + 2*4*x^2/2! + 10*4^2*x^3/3! + 92*4^3*x^4/4! + 1351*4^4*x^5/5! +...

where

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

PROG

(PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=1, n, tanh(m*X)^m); n!/4^(n-1)*polcoeff(Egf, n)}

CROSSREFS

Sequence in context: A108209 A111773 A289020 * A336271 A181084 A063385

Adjacent sequences:  A195412 A195413 A195414 * A195416 A195417 A195418

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 17 2011

STATUS

approved

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Last modified August 14 13:57 EDT 2020. Contains 336481 sequences. (Running on oeis4.)