A206531 a(n) = (2*(n+1)*(2*n+1)-1)*a(n-1) + 2*n*(2*n-1)*a(n-2), a(0)=0, a(1)=2.

0, 2, 58, 3250, 292498, 38609738, 7026972314, 1686473355362, 516060846740770, 196103121761492602, 90599642253809582122, 50011002524102889331346, 32507151640666878065374898, 24575406640344159817423422890

Offset: 0

Author

Seiichi Kirikami, Feb 11 2012

Keywords

• nonn

Comments

The numerators of the fractions limiting to the value of A206533.

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. A002939, A082108, A206532, A206533.

Programs

Magma

[n le 2 select 2*(n-1) else (2*n*(2*n-1)-1)*Self(n-1) + 2*(n-1)*(2*n-3)*Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 21 2022

Mathematica

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

SageMath

@CachedFunction
def a(n): # a = A206531
    if (n<2): return 2*n
    else: return (2*(n+1)*(2*n+1)-1)*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) = A082108(n)*a(n-1) + A002939(n)*a(n-2), a(0) = 0, a(1) = 2.