A123197 (2*n+1)*(n+1)*(2*n^2+3*n-1).

-1, 24, 195, 728, 1935, 4224, 8099, 14160, 23103, 35720, 52899, 75624, 104975, 142128, 188355, 245024, 313599, 395640, 492803, 606840, 739599, 893024, 1069155, 1270128, 1498175, 1755624, 2044899, 2368520, 2729103, 3129360, 3572099, 4060224, 4596735, 5184728, 5827395, 6528024

Offset

0,2

References

Fredrick T. Wall, Chemical Thermodynamics, W. H, Freeman, San Francisco, 1965, page 269

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n)-a(n-1) = (4*n + 1)*(4*n^2 + 2*n - 1).

G.f.: (-1+29*x+65*x^2+3*x^3)/(1-x)^5. [Colin Barker, Jan 28 2012]

a(0)=-1, a(1)=24, a(2)=195, a(3)=728, a(4)=1935, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, May 29 2014

Mathematica

f[m_] = Sum[(4*n + 1)*(4*n^2 + 2*n - 1), {n, 0, m}]; a = Table[f[n], {n, 0, 50}]
Table[(2n+1)(n+1)(2n^2+3n-1), {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {-1, 24, 195, 728, 1935}, 40] (* Harvey P. Dale, May 29 2014 *)

Crossrefs

Sequence in context: A042114 A220296 A282286 * A211151 A125361 A126519

Adjacent sequences: A123194 A123195 A123196 * A123198 A123199 A123200

Keyword

sign,easy

Author

Roger L. Bagula, Oct 04 2006

Extensions

Definition made precise by the Assoc. Eds. of the OEIS, Mar 27 2010

Status

approved