A376096 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1)^3 * a(k) * a(n-k-1).

1, 1, 9, 260, 17215, 2189997, 477731884, 164858203944, 84745577983095, 61951785517193675, 62077057930391945969, 82749694746019635920952, 143157935882304543684640676, 314805573970543375502985796300, 864458294787075036217714712292600, 2919280453922974335841433174057739408

Offset: 0

Author

Ilya Gutkovskiy, Sep 10 2024

Keywords

• nonn

Crossrefs

Cf. A000699, A015084, A088716, A256019, A376095, A376097.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(k + 1)^3 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 15}]
nmax = 15; A[] = 0; Do[A[x] = 1 + x A[x]^2 + 7 x^2 A[x] A'[x] + 6 x^3 A[x] A''[x] + x^4 A[x] A'''[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = 1 + x * A(x)^2 + 7 * x^2 * A(x) * A'(x) + 6 * x^3 * A(x) * A''(x) + x^4 * A(x) * A'''(x).