A351814 G.f. A(x) satisfies A(x) = 1 + x * A(x/(1 - x)^4) / (1 - x).

1, 1, 2, 8, 42, 272, 2115, 19010, 192760, 2172468, 26896081, 362184998, 5262526484, 81969555736, 1361249430071, 23989460080079, 446832403813788, 8765575657218860, 180544405959236487, 3893718987163468969, 87711985393624557487, 2059264143275898894916

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..467

Formula

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

Mathematica

nmax = 21; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)^4]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 3 k - 1, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A000110, A125273, A351813, A351815.

Sequence in context: A121635 A002874 A324961 * A078592 A225108 A052646

Adjacent sequences: A351811 A351812 A351813 * A351815 A351816 A351817

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 20 2022

Status

approved