A380502 a(n) = (7*n^6 - 21*n^5 + 55*n^4 - 75*n^3 + 70*n^2 - 36*n + 8)/8.

1, 1, 34, 370, 2179, 8791, 27586, 72514, 167245, 348949, 672706, 1216546, 2087119, 3425995, 5416594, 8291746, 12341881, 17923849, 25470370, 35500114, 48628411, 65578591, 87193954, 114450370, 148469509, 190532701, 242095426, 304802434, 380503495, 471269779, 579410866

Offset: 0

Author

Kelvin Voskuijl, Jan 25 2025

Keywords

• nonn
• easy

Comments

From a(1) onwards, first differences of A075664 (sum of next n cubes).

Links

• Kelvin Voskuijl, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A075664.

Cf. A005448 (first differences of sum of next n natural numbers), A380353 (for sum of next n squares).

Programs

Mathematica

Table[(7 * n^6 - 21 * n^5 + 55 * n^4 - 75 * n^3 + 70 * n^2 - 36 * n + 8) / 8, {n, 1, 30}]

PARI

a(n) = (7*n^6 - 21*n^5 + 55*n^4 - 75*n^3 + 70*n^2 - 36*n + 8)/8

Python

def A380502(n): return (n*(n*(n*(n*(n*(7*(n-3))+55)-75)+70)-36)>>3)+1 # Chai Wah Wu, Feb 09 2025

Formula

G.f.: (1 - 6*x + 48*x^2 + 118*x^3 + 303*x^4 + 132*x^5 + 34*x^6)/(1 - x)^7. - Stefano Spezia, Jan 28 2025