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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 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 January 27 01:46 EST 2023. Contains 359836 sequences. (Running on oeis4.)