A069079 a(n) = (2*n+1)*(2*n+2)*(2*n+4)*(2*n+5).

40, 504, 2160, 6160, 14040, 27720, 49504, 82080, 128520, 192280, 277200, 387504, 527800, 703080, 918720, 1180480, 1494504, 1867320, 2305840, 2817360, 3409560, 4090504, 4868640, 5752800, 6752200, 7876440, 9135504, 10539760, 12099960, 13827240, 15733120, 17829504

Offset: 0

Author

Benoit Cloitre, Apr 05 2002

Keywords

• easy
• nonn
• changed

References

• Konrad Knopp, Theory and application of infinite series, Dover, p. 268

Links

• Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original German edition of "Theory and Application of Infinite Series")
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A033996, A078371.

Programs

Mathematica

Table[16n^4+96n^3+196n^2+156n+40,{n,0,40}]

PARI

my(x='x+O('x^32)); Vec(-8*(5+38*x+5*x^2)/(x-1)^5) \\ Elmo R. Oliveira, Aug 28 2025

Formula

Sum_{n>=1} 1/a(n) = 1/36 Sum_{n>=1} (-1)^n/a(n) = 5/36 - log(2)/6.

From Elmo R. Oliveira, Aug 28 2025: (Start)

G.f.: 8*(5 + 38*x + 5*x^2)/(1 - x)^5.

E.g.f.: 4*exp(x)*(10 + 116*x + 149*x^2 + 48*x^3 + 4*x^4).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

a(n) = A078371(n)*A033996(n+1). (End)

Extensions

More terms from Elmo R. Oliveira, Aug 28 2025