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A193466 E.g.f.: Sum_{n>=0} x^n * Product_{k=1..n} cosh(k*x). 3
1, 1, 2, 9, 84, 965, 12750, 225967, 5241880, 139776345, 4272148890, 155402034491, 6513558987540, 304210965928597, 15965624278036342, 941149313037711975, 61160783460181817520, 4356686998946564113457, 340627068039399668576946, 29015657457166019702796787 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..150

FORMULA

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

EXAMPLE

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! +...

where

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) +...

Also,

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 +...

PROG

(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)}

CROSSREFS

Cf. A177385, A193467, A193468.

Sequence in context: A296581 A069234 A086929 * A262011 A120959 A125797

Adjacent sequences:  A193463 A193464 A193465 * A193467 A193468 A193469

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 27 2011

STATUS

approved

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Last modified May 6 15:25 EDT 2021. Contains 343586 sequences. (Running on oeis4.)