A050484 Partial sums of A051946.

1, 12, 68, 264, 810, 2112, 4884, 10296, 20163, 37180, 65208, 109616, 177684, 279072, 426360, 635664, 927333, 1326732, 1865116, 2580600, 3519230, 4736160, 6296940, 8278920, 10772775, 13884156, 17735472, 22467808, 28242984, 35245760

Offset: 0

Author

Barry E. Williams, Dec 26 1999

Keywords

• easy
• nonn

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A051946, A093562 ((5, 1) Pascal, column m=7).

Programs

Magma

[((5*n+7)*Binomial(n+6,6))/7: n in [0..60]]; // Vincenzo Librandi, Jul 30 2014

Mathematica

CoefficientList[Series[(1 + 4 x)/(1 - x)^8, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 30 2014 *)
Accumulate[CoefficientList[Series[(1+4x)/(1-x)^7,{x,0,40}],x]] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,12,68,264,810,2112,4884,10296},30] (* Harvey P. Dale, Aug 21 2020 *)

PARI

a(n)=binomial(n+6, 6)*(5*n+7)/7 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = C(n+6, 6)*(5n+7)/7.

G.f.: (1+4*x)/(1-x)^8.