A016815 a(n) = (4*n + 1)^3.

1, 125, 729, 2197, 4913, 9261, 15625, 24389, 35937, 50653, 68921, 91125, 117649, 148877, 185193, 226981, 274625, 328509, 389017, 456533, 531441, 614125, 704969, 804357, 912673, 1030301, 1157625, 1295029, 1442897, 1601613, 1771561, 1953125, 2146689, 2352637, 2571353

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000578, A016813.

Programs

Mathematica

(4*Range[0,30]+1)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{1,125,729,2197},30] (* Harvey P. Dale, Sep 01 2013 *)

Formula

Sum_{n>=0} 1/a(n) = Pi^3/64 + 7 zeta(3)/16.

a(0)=1, a(1)=125, a(2)=729, a(3)=2197, a(n)=4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). - Harvey P. Dale, Sep 01 2013

G.f.: ( 1+121*x+235*x^2+27*x^3 ) / (x-1)^4 . - R. J. Mathar, Dec 03 2015

From Stefano Spezia, Nov 01 2024: (Start)

a(n) = A000578(A016813(n)).

E.g.f.: exp(x)*(1 + 124*x + 240*x^2 + 64*x^3). (End)