A376112 -id:A376112 - cp's OEIS frontend

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

Ilya Gutkovskiy, Sep 10 2024

nonn

Cf. A000556, A015083, A376112, A376113.

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]

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

A376113 a(0) = 1; a(n) = (1/3) * Sum_{k=1..n} (4^k-1) * a(k-1) * a(n-k).

Original entry on oeis.org

1, 1, 6, 137, 11938, 4095882, 5599192492, 30588428274345, 668265444025582410, 58395039572032120897838, 20410643002515607839683651348, 28536181214271796693200339702494058, 159585939576145805663910944364491926768148, 3569877304419418296304606194938539586766279745396

Offset: 0

Ilya Gutkovskiy, Sep 10 2024

nonn

Cf. A015085, A337556, A376111, A376112.

a[0] = 1; a[n_] := a[n] = (1/3) Sum[(4^k - 1) a[k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 13}]
nmax = 13; A[] = 0; Do[A[x] = 3/(3 + x A[x] - 4 x A[4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

G.f. A(x) satisfies: A(x) = 3 / (3 + x * A(x) - 4 * x * A(4*x)).

cp's OEIS Frontend

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

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