A376097 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1)^4 * a(k) * a(n-k-1).

1, 1, 17, 1410, 364019, 228282823, 296324235500, 712075198644414, 2918094100584013255, 19151474626728425949663, 191553141880332262049655201, 2804913258838830873001491036584, 58168297154586087400230338311689652, 1661461159115675581245556180230933084340

Offset: 0

Author

Ilya Gutkovskiy, Sep 10 2024

Keywords

• nonn

Crossrefs

Cf. A000699, A015085, A088716, A256020, A376095, A376096.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(k + 1)^4 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
nmax = 13; A[] = 0; Do[A[x] = 1 + x A[x]^2 + 15 x^2 A[x] A'[x] + 25 x^3 A[x] A''[x] + 10 x^4 A[x] A'''[x] + x^5 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 + 15 * x^2 * A(x) * A'(x) + 25 * x^3 * A(x) * A''(x) + 10 * x^4 * A(x) * A'''(x) + x^5 * A(x) * A''''(x).