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A351817
G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^4) / (1 - x)^4.
5
1, 1, 5, 23, 139, 1052, 9166, 90073, 989205, 11981051, 158149438, 2255926638, 34549223880, 564898101239, 9812669832553, 180324597042263, 3492960489714519, 71092066388237562, 1516044005669227542, 33788707128788508476, 785270646437483414261, 18992014442689191510460
OFFSET
0,3
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+3*k+2,n-k-1) * a(k).
MATHEMATICA
nmax = 21; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)^4]/(1 - x)^4 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 3 k + 2, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 20 2022
STATUS
approved