A206308 a(n) = ((2*n+2)*(2*n+3) - 1)*a(n-1) + 2*n*(2*n+1)*a(n-2), a(0)=1, a(1)=19.

1, 19, 799, 57527, 6327971, 987163475, 207304329751, 56386777692271, 19284277970756683, 8099396747717806859, 4098294754345210270655, 2458976852607126162392999, 1726201750530202565999885299, 1401675821430524483591906862787

Offset: 0

Author

Seiichi Kirikami, Feb 11 2012

Keywords

• nonn
• frac

Comments

The denominators of the fractions limiting to the value of A206530.

References

• E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..220

Crossrefs

Cf. A002943, A125202, A206307, A206530.

Programs

Magma

[n le 2 select 19^(n-1) else (4*n^2+2*n-1)*Self(n-1) + 2*(n-1)*(2*n-1)*Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 21 2022

Mathematica

RecurrenceTable[{a[n]==((2n+3)(2n+2)-1)a[n-1]+2n(2n+1)a[n-2], a[0]==1, a[1]==19}, a, {n,15}]

SageMath

@CachedFunction # a = A206308
def a(n): return 19^n if (n<2) else (4*n^2+10*n+5)*a(n-1) + 2*n*(2*n+1)*a(n-2)
[a(n) for n in range(31)] # G. C. Greubel, Dec 21 2022

Formula

a(n) = A125202(n+2)*a(n-1) + A002943(n)*a(n-2), with a(0) = 1, a(1) = 19.