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A193466 E.g.f.: Sum_{n>=0} x^n * Product_{k=1..n} cosh(k*x). 3

%I

%S 1,1,2,9,84,965,12750,225967,5241880,139776345,4272148890,

%T 155402034491,6513558987540,304210965928597,15965624278036342,

%U 941149313037711975,61160783460181817520,4356686998946564113457,340627068039399668576946,29015657457166019702796787

%N E.g.f.: Sum_{n>=0} x^n * Product_{k=1..n} cosh(k*x).

%H Vaclav Kotesovec, <a href="/A193466/b193466.txt">Table of n, a(n) for n = 0..150</a>

%F E.g.f.: Sum_{n>=0} (x/2)^n * exp(-n*(n+1)*x/2) * Product_{k=1..n} (1 + exp(2*k*x)).

%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 84*x^4/4! + 965*x^5/5! + 12750*x^6/6! + 225967*x^7/7! +...

%e where

%e A(x) = 1 + x*cosh(x) + x^2*cosh(x)*cosh(2*x) + x^3*cosh(x)*cosh(2*x)*cosh(3*x) + x^4*cosh(x)*cosh(2*x)*cosh(3*x)*cosh(4*x) +...

%e Also,

%e A(x) = 1 + x*exp(-x)*(1+exp(2*x))/2 + x^2*exp(-3*x)*(1+exp(2*x))*(1+exp(4*x))/2^2 + x^3*exp(-6*x)*(1+exp(2*x))*(1+exp(4*x))*(1+exp(6*x))/2^3 +...

%o (PARI) {a(n)=local(X=x+x*O(x^n), Egf); Egf=sum(m=0, n, x^m*prod(k=1, m, cosh(k*X))); n!*polcoeff(Egf, n)}

%Y Cf. A177385, A193467, A193468.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 27 2011

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Last modified June 19 13:38 EDT 2021. Contains 345138 sequences. (Running on oeis4.)