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A209832 Expansion of the q-series Sum_{n>=0} (-1)^n*q^(n+1)*Product_{k = 1..n} (1 - q^(2*k-1)), q = exp(t), as a formal Taylor series in t. 1
1, 2, 12, 200, 6576, 353312, 28032192, 3077502080, 446470392576, 82695752049152, 19038594625539072, 5332477132779407360, 1785375992372231909376, 704147423230177089953792, 323094378183013059349757952, 170643791820813252598723543040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Compare with A158690.

LINKS

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

Hsien-Kuei Hwang, Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, arXiv:1911.06690 [math.CO], 2019.

FORMULA

E.g.f.: Sum_{n>=0} exp((n+1)*t) * Product_{k = 1..n} (exp((2*k-1)*t) - 1) = exp(t) + exp(2*t)*(exp(t) - 1) + exp(3*t)*(exp(t) - 1)*(exp(3*t) - 1) + ... = 1 + 2*t + 12*t^2/2! + 200*t^3/3! + ...

Conjectural S-fraction expansion for the o.g.f.:

1/(1-2*x/(1-4*x/(1-16*x/(1-20*x/(1-...-2*n(3*n-2)*x/(1-2*n(3*n-1)*x/(1-...

CROSSREFS

Cf. A158690.

Sequence in context: A182163 A245358 A317350 * A094157 A306715 A012598

Adjacent sequences:  A209829 A209830 A209831 * A209833 A209834 A209835

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Mar 14 2012

STATUS

approved

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Last modified October 28 21:20 EDT 2020. Contains 338064 sequences. (Running on oeis4.)