A372216 Product of n-th Pell number and n-th Catalan number: a(n) = A000129(n)*A000108(n).

1, 4, 25, 168, 1218, 9240, 72501, 583440, 4789070, 39940888, 337490426, 2883046320, 24858176900, 216046612080, 1890737146125, 16647522481440, 147365806700310, 1310740896927000, 11708311265437710, 104989351441019760, 944739578390934300, 8528220298405863120

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Vladimir V. Kruchinin and Maria Y. Perminova, Identities and Hadamard Product of the Generalized Fibonacci, Lucas, Catalan, and Harmonic Numbers, Journal of Integer Sequences, Vol. 28 (2025), Article 25.8.8. See p. 15.

Formula

G.f.: 1/(2*x)-sqrt(sqrt(-16*x^2-8*x+1)+4*x+3)/(4*x).

D-finite with recurrence n*(n+1)*a(n) - 4*n*(2*n-1)*a(n-1) - 4*(2*n-1)*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Apr 24 2024

a(n) ~ 2^(2*n-3/2) * (1+sqrt(2))^n / (n^(3/2) * sqrt(Pi)). - Amiram Eldar, Oct 01 2025

Mathematica

CoefficientList[Series[1/(2*x)-Sqrt[Sqrt[-16*x^2-8*x+1]+4*x+3]/(4*x), {x, 0, 20}], x] (* Stefano Spezia, Apr 22 2024 *)

Crossrefs

Cf. A000108, A000129.

Sequence in context: A074422 A390359 A128419 * A226945 A225137 A229255

Adjacent sequences: A372213 A372214 A372215 * A372217 A372218 A372219

Keyword

nonn,easy

Author

Vladimir Kruchinin, Apr 22 2024

Status

approved