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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

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

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

Cf. A202516, A155200, A155201, A155202.

Sequence in context: A209468 A270872 A141077 * A221901 A096721 A301466

Adjacent sequences:  A202514 A202515 A202516 * A202518 A202519 A202520

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 20 2011

STATUS

approved

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Last modified July 7 16:09 EDT 2020. Contains 335496 sequences. (Running on oeis4.)