A257055 a(n) = n*(n + 1)*(n^2 - n + 3)/6.

0, 1, 5, 18, 50, 115, 231, 420, 708, 1125, 1705, 2486, 3510, 4823, 6475, 8520, 11016, 14025, 17613, 21850, 26810, 32571, 39215, 46828, 55500, 65325, 76401, 88830, 102718, 118175, 135315, 154256, 175120, 198033, 223125, 250530, 280386, 312835, 348023, 386100

Offset: 0

Author

Bruno Berselli, Apr 15 2015

Keywords

• nonn
• easy

Comments

Partial sums of A037235.

After 0, this sequence is the 2nd diagonal of the square array in A080851.

For n > 2, a(n)-n is the 4th column of the triangular array in A208657.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000332, A037235, A080851, A208657.

Cf. similar sequences listed in A256859.

Programs

Magma

[n*(n+1)*(n^2-n+3)/6: n in [0..40]];

Mathematica

Table[n (n + 1) (n^2 - n + 3)/6, {n, 40}]

PARI

vector(40, n, n--; n*(n+1)*(n^2-n+3)/6)

Sage

[n*(n+1)*(n^2-n+3)/6 for n in (0..40)]

Formula

G.f.: x*(1 + 3*x^2)/(1 - x)^5.

a(n) = 3*A000332(n+1) + A000332(n+3).

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, May 27 2021