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A202517 G.f.: exp( Sum_{n>=1} (3^n - 2^n)^n * x^n/n ). 1
1, 1, 13, 2299, 4465027, 83649932869, 14413888012788031, 22412828378864422506133, 312169717565869706933620630009, 38865154523992131836783382601539858727, 43266472789023671032936589458127528396392744933 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
More generally, for integers p and q, exp( Sum_{n>=1} (p^n - q^n)^n * x^n/n ) is a power series in x with integer coefficients.
LINKS
EXAMPLE
G.f.: A(x) = 1 + x + 13*x^2 + 2299*x^3 + 4465027*x^4 + 83649932869*x^5 +...
where
log(A(x)) = (3-2)*x + (3^2 - 2^2)^2*x^2/2 + (3^3 - 2^3)^3*x^3/3 + (3^4 - 2^4)^4*x^4/4 + (3^5 - 2^5)^5*x^5/5 +...
more explicitly,
log(A(x)) = x + 5^2*x^2/2 + 19^3*x^3/3 + 65^4*x^4/4 + 211^5*x^5/5 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (3^m-2^m)^m*x^m/m)+x*O(x^n)), n)}
CROSSREFS
Sequence in context: A209468 A270872 A141077 * A221901 A096721 A301466
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 20 2011
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)