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

0,2

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..33.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

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

Mathematica

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

Crossrefs

Cf. A051947.

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

Sequence in context: A076676 A044149 A044530 * A066999 A224291 A055826

Adjacent sequences: A050480 A050481 A050482 * A050484 A050485 A050486

Keyword

easy,nonn

Author

Barry E. Williams, Dec 26 1999

Status

approved