A281861 Riordan transform of the Fibonacci sequence with the Riordan matrix A053121.

0, 1, 1, 4, 6, 18, 32, 85, 165, 411, 839, 2013, 4237, 9933, 21317, 49236, 107014, 244750, 536500, 1218888, 2687362, 6077644, 13453606, 30329434, 67326816, 151439158, 336842092, 756452890, 1684953360, 3779590010, 8427441240

Offset

0,4

Comments

The Riordan matrix A053121 of the Bell type R = (c(x^2), x*c(x^2)), with the o.g.f. c of A000108 (Catalan), is the inverse of the Riordan matrix A049310 (Chebyshev S).

The Riordan transform of a sequence {a_n}, n >= 0 to a sequence {b_n}, n >= 0 is b = R a

in matrix notation, with the lower triangular Riordan matrix (N x N, with arbitrary large N).

Links

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

Formula

G.f.: c(x^2)*A(x*c(x^2)) with the g.f. c of A000108 (Catalan) and A of A000045 (Fibonacci).

a(n) = Sum_{m=0..n} R(n, m)*F(n), with R(n, m) = A053121(n, m) and F(m) = A000045(m), n >= 0.

Crossrefs

Cf. A000045, A000108, A049310, A053121, A014019.

Sequence in context: A209236 A182643 A156096 * A218898 A088810 A005199

Adjacent sequences: A281858 A281859 A281860 * A281862 A281863 A281864

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 18 2017

Status

approved