A156336 -id:A156336 - cp's OEIS frontend

A156335 G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.

1, 2, 4, 16, 92, 1816, 47344, 4888640, 546663016, 245429690704, 113080892367776, 209848258185362560, 393950238751186551328, 2976605303522286162203456, 22642571073509592590956639360, 692351532949951721637759480882688

Offset: 0

Paul D. Hanna, Feb 10 2009

nonn

			G.f.: A(x) = 1 + 2*x + 4*x^2 + 16*x^3 + 92*x^4 + 1816*x^5 + 47344*x^6 +...
log(A(x)) = 2*x + 2^2*x^2/2 + 2^5*x^3/3 + 2^8*x^4/4 + 2^13*x^5/5 + 2^18*x^6/6 +...

Cf. A156334, A156336, A156337, A155200.

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

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

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.

Original entry on oeis.org

1, 4, 16, 384, 17856, 13492992, 11507268608, 160888878129152, 2306486569154275328, 537309590223329223155712, 126767209261235580163634135040, 483356141899716284828508078471905280

Offset: 0

Paul D. Hanna, Feb 10 2009

nonn

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.

			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 +...

Cf. A156335, A156336, A155207, A155200.

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

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

cp's OEIS Frontend

A156335 G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.

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