A372210 Product of n!, n-th Pell number and n-th harmonic number.

1, 6, 55, 600, 7946, 123480, 2208492, 44710272, 1011177360, 25274905920, 692042185440, 20602098316800, 662620120237440, 22898921925035520, 846245264387040000, 33303963647943475200, 1390631677349880268800, 61407154400075559936000, 2859166138267857522585600

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

E.g.f.: (2*x*log(-x^2-2*x+1)+(sqrt(2)-sqrt(2)*x)*log(-((sqrt(2)+1)*x-1) / ((sqrt(2)-1)*x+1)))/(4*(x^2+2*x-1)).

a(n) = n!*A000129(n)*A001008(n)/A002805(n).

D-finite with recurrence 8*a(n) +16*(-2*n+1)*a(n-1) +(16*n^2-32*n+25)*a(n-2) +4*(8*n^3-36*n^2+47*n-13)*a(n-3) +2*(2*n-5)*(2*n^3-11*n^2+17*n-7)*a(n-4) +4*(n-4)^3*a(n-5) +(n-4)^2*(n-5)^2*a(n-6)=0. - R. J. Mathar, Apr 24 2024

Crossrefs

Cf. A000129, A000142, A000254, A001008, A002805, A052631.

Sequence in context: A118836 A079589 A371776 * A365840 A006200 A243691

Adjacent sequences: A372206 A372207 A372208 * A372211 A372212 A372213

Keyword

nonn

Author

Vladimir Kruchinin, Apr 22 2024

Status

approved