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

0,2

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).

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)

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 *)

Crossrefs

Cf. A034263.

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

Sequence in context: A163716 A271662 A244864 * A274561 A253221 A222633

Adjacent sequences: A051944 A051945 A051946 * A051948 A051949 A051950

Keyword

easy,nonn

Author

Barry E. Williams, Dec 21 1999

Extensions

Corrected by T. D. Noe, Nov 09 2006

Status

approved