A206307 a(n) = ((2*n+2)*(2*n+3) - 1)*a(n-1) + 2*n*(2*n+1)*a(n-2), a(0)=0, a(1)=6.

0, 6, 246, 17718, 1948974, 304039950, 63848389494, 17366761942374, 5939432584291902, 2494561685402598846, 1262248212813715016070, 757348927688229009642006, 531658947237136764768688206, 431707065156555052992174823278

Offset: 0

Author

Seiichi Kirikami, Feb 11 2012

Keywords

• nonn

Comments

The numerators 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, A206308, A206530.

Programs

Magma

[n le 2 select 6*(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 20 2022

Mathematica

RecurrenceTable[{a[n]==((2n+3)(2n+2)-1)a[n-1]+2n(2n+1)a[n-2],a[0]==0,a[1]==6},a,{n,15}]

SageMath

@CachedFunction
def a(n): return 6*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 20 2022

Formula

a(n) = A125202(n+2)*a(n-1) + A002943(n)*a(n-2), a(0) = 0, a(1) = 6.