A351815 -id:A351815 - cp's OEIS frontend

A351818 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^5) / (1 - x)^5.

1, 1, 6, 31, 211, 1841, 18547, 210664, 2682657, 37807531, 581985596, 9696297528, 173702897000, 3327063115248, 67790086866271, 1462900566163696, 33310115601839624, 797687851718024035, 20032231443590167914, 526189230537615409571, 14423255501358439152231

Offset: 0

Ilya Gutkovskiy, Feb 20 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..452

Cf. A000110, A045500, A125274, A351815, A351816, A351817.

nmax = 20; A[] = 0; Do[A[x] = 1 + x A[x/(1 - x)^5]/(1 - x)^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 4 k + 3, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 20}]

a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+4*k+3,n-k-1) * a(k).

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

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Feb 20 2022

nonn

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

Cf. A000110, A125273, A351813, A351815.

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}]

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

cp's OEIS Frontend

A351818 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^5) / (1 - x)^5.

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