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

Author

Wolfdieter Lang, Feb 18 2017

Keywords

• nonn
• easy

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).

Crossrefs

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

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.