A376127 a(n) = 1 + Sum_{k=0..n-1} (k+1)^3 * a(k) * a(n-k-1).
1, 2, 19, 565, 38056, 4886164, 1071397370, 370880032881, 191040201050842, 139853547948358801, 140279102716474353325, 187136598610376840549341, 323937672908434382002891895, 712668454800648677607151322833, 1957709831409075714559805601326566, 6613164804688226108094777888275765585
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Keywords
Programs
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Mathematica
a[n_] := a[n] = 1 + 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/((1 - x) (1 - x A[x] - 7 x^2 A'[x] - 6 x^3 A''[x] - x^4 A'''[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Formula
G.f. A(x) satisfies: A(x) = 1 / ( (1 - x) * (1 - x * A(x) - 7 * x^2 * A'(x) - 6 * x^3 * A''(x) - x^4 * A'''(x)) ).