A373622 a(n) = A000032(n)*A000045(n)*A000108(n).

0, 1, 6, 40, 294, 2310, 19008, 161733, 1411410, 12563408, 113624940, 1041158846, 9645100416, 90182859700, 849966450840, 8066498833800, 77019930780030, 739349587508730, 7131313919822400, 69079082238199110, 671733716498945100, 6554862704411317920, 64166669054324268120, 629964451984076275950

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Vladimir V. Kruchinin and Maria Y. Perminova, Identities and Generating Functions of Products of Generalized Fibonacci numbers, Catalan and Harmonic Numbers, arXiv:2406.02937 [math.CO], 2024.

Formula

G.f.: (sqrt((-2*sqrt(16*x^2 - 12*x + 1) - 42*x + 7)/5 + 6*x) - 1)/(2*x).

D-finite with recurrence n*(n+1)*a(n) -6*n*(2*n-1)*a(n-1) +4*(2*n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Jun 12 2024

Maple

gf := (sqrt(-10*sqrt(16*x^2 - 12*x + 1) - 60*x + 35) - 5) / (10*x):
ser := series(gf, x, 32): seq(coeff(ser, x, n), n = 0..22);
# Peter Luschny, Jun 11 2024

Mathematica

CoefficientList[Series[(Sqrt[(-2*Sqrt[16*x^2-12*x+1]-42*x+7)/5+6*x]-1)/(2*x), {x, 0, 23}], x] (* Stefano Spezia, Jun 11 2024 *)

Crossrefs

Cf. A000032, A000045, A000108, A119694.

Sequence in context: A081337 A316912 A366199 * A138240 A358598 A083805

Adjacent sequences: A373619 A373620 A373621 * A373623 A373624 A373626

Keyword

nonn

Author

Vladimir Kruchinin, Jun 11 2024

Status

approved