A051947 Partial sums of A034263.

1, 10, 49, 168, 462, 1092, 2310, 4488, 8151, 14014, 23023, 36400, 55692, 82824, 120156, 170544, 237405, 324786, 437437, 580888, 761530, 986700, 1264770, 1605240, 2018835, 2517606, 3115035, 3826144, 4667608, 5657872, 6817272, 8168160, 9735033, 11544666

Offset: 0

Author

Barry E. Williams, Dec 21 1999

Keywords

• easy
• nonn

References

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A034263.

Cf. A093561 ((4, 1) Pascal, column m=6).

Programs

Mathematica

Nest[Accumulate,Range[1,160,4],5] (* Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,10,49,168,462,1092,2310},40] (* Harvey P. Dale, Nov 08 2024 *)

Formula

a(n) = C(n+5, 5)*(2n+3)/3.

G.f.: (1+3*x)/(1-x)^7.

From Amiram Eldar, Feb 15 2022: (Start)

Sum_{n>=0} 1/a(n) = 2161/28 - 768*log(2)/7.

Sum_{n>=0} (-1)^n/a(n) = 192*Pi/7 - 624*log(2)/7 - 657/28. (End)

Extensions

Corrected by T. D. Noe, Nov 09 2006