A372199 a(n) = n! * F(n) * H(n), where F(n) is the n-th Fibonacci number and H(n) the n-th harmonic number.

1, 3, 22, 150, 1370, 14112, 169884, 2301264, 34903584, 584575200, 10728401760, 214047774720, 4614042856320, 106866549054720, 2646889430976000, 69814736722483200, 1953778728154982400, 57822137143219814400, 1804373878844546150400, 59213693468692224000000

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

E.g.f.: (5*x*log(-x^2 - x + 1) - sqrt(5)*(x - 2)*(log(2 - (sqrt(5) + 1)*x) -log((sqrt(5) - 1)*x + 2))) / (10*x*(x^2 + x - 1)).

a(n) = n! * A000045(n) * A001008(n) / A002805(n).

a(n) = A000045(n) * A000254(n) / A002805(n). - R. J. Mathar, Apr 24 2024

D-finite with recurrence 5*a(n) +5*(-2*n+1)*a(n-1) +(-5*n^2+10*n+1)*a(n-2) +(10*n^3-45*n^2+58*n-14)*a(n-3) +(5*n^4-40*n^3+109*n^2-108*n+16)*a(n-4) +2*(n-4)^3*a(n-5) +(n-4)^2*(n-5)^2*a(n-6)=0. - R. J. Mathar, Apr 24 2024

Maple

H := proc(n)
    add(1/i, i=1..n) ;
end proc:
A372199 := proc(n)
    n!*A000045(n)*H(n) ;
end proc:
seq(A372199(n), n=1..70) ; # R. J. Mathar, Apr 24 2024

Mathematica

a[n_] := n! Fibonacci[n] HarmonicNumber[n]; Array[a, 20] (* Stefano Spezia, Apr 22 2024 *)

Crossrefs

Cf. A000045, A001008, A002805.

Sequence in context: A156089 A110469 A121723 * A037775 A037663 A091167

Adjacent sequences: A372195 A372197 A372198 * A372200 A372201 A372202

Keyword

nonn

Author

Vladimir Kruchinin, Apr 21 2024

Status

approved