Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #5 Sep 11 2024 00:44:43
%S 1,1,4,35,600,19942,1299768,167796051,43131308656,22127283690338,
%T 22680691426392504,46472849736334410494,190399379929624643874384,
%U 1559942353285454499773312748,25559656412925984160985399396784,837564388804449970974724247002202883
%N a(0) = 1; a(n) = Sum_{k=1..n} (2^k-1) * a(k-1) * a(n-k).
%F G.f. A(x) satisfies: A(x) = 1 / (1 + x * A(x) - 2 * x * A(2*x)).
%t a[0] = 1; a[n_] := a[n] = Sum[(2^k - 1) a[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]
%t nmax = 15; A[_] = 0; Do[A[x_] = 1/(1 + x A[x] - 2 x A[2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A000556, A015083, A376112, A376113.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 10 2024