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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. 2
1, 2, 4, 16, 92, 1816, 47344, 4888640, 546663016, 245429690704, 113080892367776, 209848258185362560, 393950238751186551328, 2976605303522286162203456, 22642571073509592590956639360, 692351532949951721637759480882688 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = (1/n)*Sum_{k=1..n} 2^floor((k^2+1)/2) * a(n-k) for n>0, with a(0)=1.
EXAMPLE
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 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(k=1, n, 2^floor((k^2+1)/2)*x^k/k)+x*O(x^n)), n)}
CROSSREFS
Sequence in context: A291286 A007171 A058136 * A026089 A052835 A009565
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 10 2009
STATUS
approved

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Last modified July 14 20:49 EDT 2024. Contains 374323 sequences. (Running on oeis4.)