A352904 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n,4*k+1) * a(k).

1, 1, 2, 3, 4, 6, 12, 28, 64, 137, 282, 583, 1244, 2733, 6062, 13343, 28944, 61969, 131602, 278483, 588564, 1242646, 2618924, 5505556, 11542528, 24142217, 50409898, 105154719, 219278860, 457362189, 954629598, 1994940799, 4175986720, 8760742945, 18428667938

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Formula

G.f. A(x) satisfies: A(x) = 1 + x * A(x^4/(1 - x)^4) / (1 - x)^2.

E.g.f.: 1 + exp(x) * Sum_{n>=0} a(n) * x^(4*n+1) / (4*n+1)!.

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 4 k + 1] a[k], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 34}]
nmax = 34; A[_] = 0; Do[A[x_] = 1 + x A[x^4/(1 - x)^4]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A040027, A119685, A352066, A352879.

Sequence in context: A078495 A161701 A038504 * A275448 A018405 A018419

Adjacent sequences: A352901 A352902 A352903 * A352905 A352906 A352907

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 07 2022

Status

approved