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 A363441 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (2*x)^k/k ). 3
 1, 2, 4, 16, 52, 208, 840, 3520, 15008, 65344, 288408, 1288416, 5813744, 26460800, 121333200, 559991712, 2599385536, 12127405952, 56837861376, 267473333120, 1263354463056, 5987210061184, 28461008374480, 135672151034304, 648406644570048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+2*x^(k+1))^a(k). a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-2)^(k/d) * a(d-1) ) * a(n-k). PROG (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, x^k)*(2*x)^k/k)+x*O(x^n))); Vec(A); CROSSREFS Cf. A004111, A363442, A363443. Cf. A179469, A363425. Sequence in context: A153948 A284730 A255730 * A010362 A262164 A322940 Adjacent sequences: A363438 A363439 A363440 * A363442 A363443 A363444 KEYWORD nonn AUTHOR Seiichi Manyama, Jun 02 2023 STATUS approved

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Last modified April 22 21:44 EDT 2024. Contains 371906 sequences. (Running on oeis4.)