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A215066 E.g.f.: Sum_{n>=0} Product_{k=1..n} (exp((2*k-1)*x) - 1). 5
1, 1, 7, 127, 4315, 235831, 18911467, 2091412807, 305035062955, 56729101908151, 13102338649018027, 3679320979659518887, 1234515698986458346795, 487763952468349266962071, 224150079034073231822617387, 118541831524545132821950527367 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

A. Folsom, K. Ono and R. C. Rhoades, Ramanujan's radial limits, http://math.stanford.edu/~rhoades/FILES/ramanujans_radial.pdf, 2013. - From N. J. A. Sloane, Feb 09 2013

LINKS

Table of n, a(n) for n=0..15.

FORMULA

Folsom et al. give a closed form for a(n). - N. J. A. Sloane, Feb 09 2013

E.g.f.: 1 + (exp(x)-1)/(W(0)-exp(x)+1), where W(k) = (exp(x))^(2*k+1) - ((exp(x))^(2*k+3)-1)/W(k+1); (continued fraction). - Sergei N. Gladkovskii, Jan 05 2014

a(n) ~ sqrt(6) * 24^n * (n!)^2 / (sqrt(n) * Pi^(2*n+3/2)). - Vaclav Kotesovec, May 04 2014

E.g.f.: 1/2*( 1 + Sum_{n>=0} exp((2*n+1)*x)*Product_{k=1..n} (exp((2*k-1)*x) - 1) ). Cf. A053250 and A207569. - Peter Bala, May 15 2017

EXAMPLE

E.g.f.: A(x) = 1 + x + 7*x^2/2! + 127*x^3/3! + 4315*x^4/4! + 235831*x^5/5! +...

where

A(x) = 1 + (exp(x)-1) + (exp(x)-1)*(exp(3*x)-1) + (exp(x)-1)*(exp(3*x)-1)*(exp(5*x)-1) + (exp(x)-1)*(exp(3*x)-1)*(exp(5*x)-1)*(exp(7*x)-1) + (exp(x)-1)*(exp(3*x)-1)*(exp(5*x)-1)*(exp(7*x)-1)*(exp(9*x)-1) +...

MATHEMATICA

Table[((-1)^n*2*Sum[Sum[n!/(a!*(2b)!*(n-a-2b)!)*(3/2)^a*(5/2)^(2b) * EulerE[2a+2b], {a, 0, n}], {b, 0, n/2}] + 2*(-1)^n*Sum[n!/((n-2b)!*(2b)!)*(3/2)^(n-2b)*(1/2)^(2b)*EulerE[2n-2b], {b, 0, n/2}])/4, {n, 0, 20}] (* Vaclav Kotesovec, May 04 2014 after A. Folsom *)

PROG

(PARI) {a(n)=n!*polcoeff(sum(m=0, n+1, prod(k=1, m, exp((2*k-1)*x+x*O(x^n))-1)), n)}

for(n=0, 26, print1(a(n), ", "))

CROSSREFS

Cf. A214687, A158690, A053250, A207569.

Sequence in context: A241955 A139291 A274673 * A092676 A002067 A274571

Adjacent sequences:  A215063 A215064 A215065 * A215067 A215068 A215069

KEYWORD

nonn,easy

AUTHOR

Paul D. Hanna, Aug 01 2012

STATUS

approved

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Last modified April 24 19:49 EDT 2019. Contains 322446 sequences. (Running on oeis4.)