A352864 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-k,k) * a(n-2*k-1).

1, 1, 1, 3, 6, 13, 34, 84, 230, 653, 1893, 5794, 18080, 58345, 193761, 657959, 2295398, 8177305, 29775086, 110676222, 419169483, 1617868052, 6353518921, 25376986471, 103017630200, 424704411564, 1777458163195, 7546547411488, 32490058003914, 141774055915497, 626739661952337

Offset

0,4

Links

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

Formula

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

Mathematica

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

Crossrefs

Cf. A040027, A172383, A352865.

Sequence in context: A361932 A201951 A104448 * A062466 A366940 A053564

Adjacent sequences: A352861 A352862 A352863 * A352865 A352866 A352867

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 06 2022

Status

approved