A156212 G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*A000204(n)*x^n/n ), a power series in x with integer coefficients.

1, 2, 26, 732, 116390, 74067484, 206309321188, 2332635556428984, 108379291296448423558, 20417630652420537229303340, 15592143220454380480367922739340

Offset

0,2

Comments

Compare to g.f. of Fibonacci sequence: exp( Sum_{n>=1} A000204(n)*x^n/n ), where A000204 is the Lucas numbers.

Links

Table of n, a(n) for n=0..10.

Example

G.f.: A(x) = 1 + 2*x + 26*x^2 + 732*x^3 + 116390*x^4 + 74067484*x^5 +...
log(A(x)) = 2*x + 2^4*3*x^2/2 + 2^9*4*x^3/3 + 2^16*7*x^4/4 + 2^25*11*x^5/5 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, 2^(m^2)*(fibonacci(m+1)+fibonacci(m-1))*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A000045, A000204.

Sequence in context: A371297 A206601 A156211 * A138524 A329556 A316747

Adjacent sequences: A156209 A156210 A156211 * A156213 A156214 A156215

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2009

Status

approved