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 A322209 L.g.f.: log( Product_{n>=1} 1/(1 - (2^n+1)*x^n) ). 3
 0, 3, 19, 54, 199, 408, 1612, 3090, 11023, 26487, 80994, 199686, 676540, 1700832, 5285096, 15197274, 45739039, 131368404, 401655943, 1172222958, 3549402474, 10533769146, 31617172980, 94336116834, 283990486780, 848323147233, 2546924693306, 7631598676410, 22903854049016, 68645946621360, 206035134959112, 617739968277066, 1853594327953471 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = Sum_{k=0..n} A322200(n-k,k) * 2^k for n >= 0. EXAMPLE L.g.f.: L(x) = 3*x + 19*x^2/2 + 54*x^3/3 + 199*x^4/4 + 408*x^5/5 + 1612*x^6/6 + 3090*x^7/7 + 11023*x^8/8 + 26487*x^9/9 + 80994*x^10/10 + 199686*x^11/11 + 676540*x^12/12 + ... such that exp( L(x) ) = 1 + 3*x + 14*x^2 + 51*x^3 + 195*x^4 + 663*x^5 + 2345*x^6 + 7707*x^7 + 25744*x^8 + 82980*x^9 + 267812*x^10 + 846150*x^11 + 2676163*x^12 + ... + A322199(n)*x^n + ... also, exp( L(x) ) = 1/( (1 - 3*x) * (1 - 5*x^2) * (1 - 9*x^3) * (1 - 17*x^4) * (1 - 33*x^5) * (1 - 65*x^6) * (1 - 129*x^7) * ... * (1 - (2^n+1)*x^n) * ... ). PROG (PARI) {L = sum(n=1, 41, -log(1 - (x^n + y^n) +O(x^41) +O(y^41)) ); } {A322200(n, k) = polcoeff( (n+k)*polcoeff( L, n, x), k, y)} {a(n) = sum(k=0, n, A322200(n-k, k)*2^k )} for(n=0, 40, print1( a(n), ", ") ) CROSSREFS Cf. A322200, A322199. Sequence in context: A265774 A100697 A134268 * A088798 A027272 A337648 Adjacent sequences: A322206 A322207 A322208 * A322210 A322211 A322212 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 01 2018 STATUS approved

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Last modified March 20 05:51 EDT 2023. Contains 361359 sequences. (Running on oeis4.)