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A156337 G.f.: A(x) = exp( Sum_{n>=1} 4^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients. 2
1, 4, 16, 384, 17856, 13492992, 11507268608, 160888878129152, 2306486569154275328, 537309590223329223155712, 126767209261235580163634135040, 483356141899716284828508078471905280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

It appears that g.f. exp( Sum_{n>=1} m^[(n^2+1)/2]*x^n/n ) forms a power series in x with integer coefficients for any positive integer m.

LINKS

Table of n, a(n) for n=0..11.

FORMULA

a(n) = (1/n)*Sum_{k=1..n} 4^floor((k^2+1)/2) * a(n-k) for n>0, with a(0)=1.

EXAMPLE

G.f.: A(x) = 1 + 4*x + 16*x^2 + 384*x^3 + 17856*x^4 + 13492992*x^5 +...

log(A(x)) = 4*x + 4^2*x^2/2 + 4^5*x^3/3 + 4^8*x^4/4 + 4^13*x^5/5 + 4^18*x^6/6 +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, 4^floor((k^2+1)/2)*x^k/k)+x*O(x^n)), n)}

CROSSREFS

Cf. A156335, A156336, A155207, A155200.

Sequence in context: A207851 A202681 A067211 * A000874 A061580 A037976

Adjacent sequences:  A156334 A156335 A156336 * A156338 A156339 A156340

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 10 2009

STATUS

approved

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Last modified June 25 03:35 EDT 2021. Contains 345449 sequences. (Running on oeis4.)