A090393 Eighth diagonal (m=7) of triangle A084938; a(n) = A084938(n+7,n) = (n^7 + 63*n^6 + 1855*n^5 + 34125*n^4 + 438424*n^3 + 3980172*n^2 + 20946960*n)/5040.

0, 5040, 12288, 22572, 36992, 56990, 84432, 121703, 171816, 238536, 326520, 441474, 590328, 781430, 1024760, 1332165, 1717616, 2197488, 2790864, 3519864, 4410000, 5490558, 6795008, 8361443, 10233048, 12458600, 15093000, 18197838

Offset: 0

Author

Philippe Deléham, Jan 31 2004

Keywords

• easy
• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A084938 A090238.

Programs

Python

A090393_list, m = [], [1, 6, 25, 92, 327, 1142, 3447, 0]
for _ in range(1001):
    A090393_list.append(m[-1])
    print(m[-1])
    for i in range(7):
        m[i+1] += m[i] # Chai Wah Wu, Jun 04 2016

Formula

a(n) = A084938(n+7, n) = Sum_{k=0..7} A090238(7, k)*binomial(n, k).

From Chai Wah Wu, Jun 04 2016: (Start)

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n > 7.

G.f.: x*(3447*x^6 - 21824*x^5 + 57742*x^4 - 81760*x^3 + 65388*x^2 - 28032*x + 5040)/(x - 1)^8. (End)