A376111 a(0) = 1; a(n) = Sum_{k=1..n} (2^k-1) * a(k-1) * a(n-k).

1, 1, 4, 35, 600, 19942, 1299768, 167796051, 43131308656, 22127283690338, 22680691426392504, 46472849736334410494, 190399379929624643874384, 1559942353285454499773312748, 25559656412925984160985399396784, 837564388804449970974724247002202883

Offset: 0

Author

Ilya Gutkovskiy, Sep 10 2024

Keywords

• nonn

Crossrefs

Cf. A000556, A015083, A376112, A376113.

Programs

Mathematica

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}]
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]

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 + x * A(x) - 2 * x * A(2*x)).