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

Offset: 1

Author

Vladimir Kruchinin, Apr 22 2024

Keywords

• nonn

Crossrefs

Cf. A000108, A000129.

Programs

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 *)

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