A351660 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 * A(x/(1 - x)) / (1 - x)^2.

1, 1, 1, 1, 3, 7, 15, 33, 81, 225, 679, 2139, 6931, 23185, 80809, 295141, 1128487, 4492363, 18506923, 78584193, 343414489, 1544535129, 7151822771, 34086446307, 167058478355, 840700482197, 4337529697349, 22915761303125, 123863743341203, 684588061704611, 3867278506969535

Offset

0,5

Links

Table of n, a(n) for n=0..30.

Formula

a(0) = a(1) = a(2) = 1; a(n) = Sum_{k=0..n-3} binomial(n-2,k+1) * a(k).

Mathematica

nmax = 30; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = If[n < 3, 1, Sum[Binomial[n - 2, k + 1] a[k], {k, 0, n - 3}]]; Table[a[n], {n, 0, 30}]

Crossrefs

Cf. A040027, A210540, A351437, A351707.

Sequence in context: A225338 A101892 A211279 * A199882 A147102 A147379

Adjacent sequences: A351657 A351658 A351659 * A351661 A351662 A351663

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 16 2022

Status

approved