A050483 Partial sums of A051947.

1, 11, 60, 228, 690, 1782, 4092, 8580, 16731, 30745, 53768, 90168, 145860, 228684, 348840, 519384, 756789, 1081575, 1519012, 2099900, 2861430, 3848130, 5112900, 6718140, 8736975, 11254581, 14369616, 18195760, 22863368, 28521240, 35338512, 43506672, 53241705, 64786371

Offset: 0

Author

Barry E. Williams, Dec 26 1999

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 (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A051947.

Cf. A093561 ((4, 1) Pascal, column m=7).

Programs

Mathematica

Table[(4*n + 7)*Binomial[n + 6, 6]/7, {n, 0, 40}] (* Amiram Eldar, Feb 15 2022 *)

Formula

a(n) = C(n+6, 6)*(4n+7)/7.

G.f.: (1+3*x)/(1-x)^8. - proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009

Sum_{n>=0} 1/a(n) = 57344*Pi/663 - 114688*log(2)/221 + 295372/3315. - Amiram Eldar, Feb 15 2022