A206532 a(n) = (2(n+1)(2n+1)-1) * a(n-1) + 2n(2n-1) * a(n-2), a(0) = 1, a(1) = 11.

1, 11, 331, 18535, 1668151, 220195931, 40075659443, 9618158266319, 2943156429493615, 1118399443207573699, 516700542761899048939, 285218699604568275014327, 185392154742969378759312551, 140156468985684850342040288555

Offset

0,2

Comments

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

References

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

Links

Robert Israel, Table of n, a(n) for n = 0..223

Formula

a(n) = A082108*a(n-1) + A002939*a(n-2), a(0) = 1, a(1) = 11.

a(n) = -4*n*(-1)^n*(n+1)*LommelS1(2*n+1/2, 3/2, 1)-2*(-1)^n*(n+1)*LommelS1(2*n+3/2, 1/2, 1)+(1-cos(1))*(2*n+2)!+(-1)^n. - Robert Israel, Sep 16 2018

Maple

f:= gfun:-rectoproc({a(n) = (2*(n+1)*(2*n+1)-1) * a(n-1) + 2*n*(2*n-1) * a(n-2), a(0) = 1, a(1) = 11}, a(n), remember):
map(f, [$0..40]); # Robert Israel, Sep 16 2018

Mathematica

RecurrenceTable[{a[n]==(2(n+1)(2n+1)-1)a[n-1]+2n(2n-1)a[n-2], a[0]==1, a[1]==11}, a, {n, 15}]

Crossrefs

Cf. A002939, A082108, A206531, A206533.

Sequence in context: A084944 A107441 A086923 * A106717 A215015 A219072

Adjacent sequences: A206529 A206530 A206531 * A206533 A206534 A206535

Keyword

nonn

Author

Seiichi Kirikami, Feb 11 2012

Status

approved