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A155209 G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n * x^n/n ), a power series in x with integer coefficients. 5
1, 3, 117, 83691, 1057319541, 224085796087563, 785909534807110163445, 45253898808490419883694669835, 42530103981310660908750359650219091445, 649533982980850199063905669772208004250784346635 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
More generally, for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.
LINKS
EXAMPLE
G.f.: A(x) = 1 + 3*x + 117*x^2 + 83691*x^3 + 1057319541*x^4 +...
log(A(x)) = 3*x + 15^2*x^2/2 + 63^3*x^3/3 + 255^4*x^4/4 + 1023^5*x^5/5 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (4^m-1)^m*x^m/m)+x*O(x^n)), n)}
CROSSREFS
Sequence in context: A097642 A009095 A326995 * A037117 A283883 A173053
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 04 2009
STATUS
approved

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Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)