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

0,2

References

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

Links

Table of n, a(n) for n=0..31.

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

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)

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 *)

Crossrefs

Cf. A027819, A050483.

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

Sequence in context: A008533 A010024 A008414 * A118979 A014970 A236967

Adjacent sequences: A052178 A052179 A052180 * A052182 A052183 A052184

Keyword

easy,nonn

Author

Barry E. Williams, Jan 26 2000

Status

approved