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A281861 Riordan transform of the Fibonacci sequence with the Riordan matrix A053121. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 13 18:45 EDT 2021. Contains 345008 sequences. (Running on oeis4.)