A052181 Partial sums of A050483.

1, 12, 72, 300, 990, 2772, 6864, 15444, 32175, 62920, 116688, 206856, 352716, 581400, 930240, 1449624, 2206413, 3287988, 4807000, 6906900, 9768330, 13616460, 18729360, 25447500, 34184475, 45439056, 59808672, 78004432, 100867800, 129389040, 164727552, 208234224

Offset: 0

Author

Barry E. Williams, Jan 26 2000

Keywords

• easy
• nonn

References

• Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A027819, A050483.

Cf. A093561 ((4, 1) Pascal, column m=8).

Programs

Maple

a:=n->(sum((numbcomp(n,8)), j=7..n))/2:seq(a(n), n=8..31); # Zerinvary Lajos, Aug 26 2008

Mathematica

Table[(n + 2)*Binomial[n + 7, 7]/2, {n, 0, 40}] (* Amiram Eldar, Feb 11 2022 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,12,72,300,990,2772,6864,15444,32175},40] (* Harvey P. Dale, Sep 06 2024 *)

Formula

a(n) = A027819(n+1)/7.

a(n) = (n+2)*C(n+7, 7)/2.

G.f.: (1+3*x)/(1-x)^9.

a(n) = C(n+2, 2)*C(n+7, 6)/7. - Zerinvary Lajos, Jul 29 2005

From Amiram Eldar, Feb 11 2022: (Start)

Sum_{n>=0} 1/a(n) = 41783/300 - 14*Pi^2.

Sum_{n>=0} (-1)^n/a(n) = 7*Pi^2 - 2688*log(2)/5 + 91343/300. (End)