A156335 -id:A156335 - cp's OEIS frontend

A156336 G.f.: A(x) = exp( Sum_{n>=1} 3^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.

1, 3, 9, 99, 1917, 324567, 65546253, 121237985007, 231991261827633, 4053251131970038227, 71801958531451566872745, 11561440390042361895766055043, 1877401313066393527954697682635421

Offset: 0

Paul D. Hanna, Feb 10 2009

nonn

			G.f.: A(x) = 1 + 3*x + 9*x^2 + 99*x^3 + 1917*x^4 + 324567*x^5 +...
log(A(x)) = 3*x + 3^2*x^2/2 + 3^5*x^3/3 + 3^8*x^4/4 + 3^13*x^5/5 + 3^18*x^6/6 +...

Cf. A156335, A156337, A155203.

{a(n)=polcoeff(exp(sum(k=1, n, 3^floor((k^2+1)/2)*x^k/k)+x*O(x^n)), n)}

a(n) = (1/n)*Sum_{k=1..n} 3^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

A156336 G.f.: A(x) = exp( Sum_{n>=1} 3^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula