A369794 Expansion of 1/(1 - x^5/(1-x)^6).

1, 0, 0, 0, 0, 1, 6, 21, 56, 126, 253, 474, 870, 1651, 3367, 7372, 16762, 38183, 85290, 185573, 394555, 826752, 1724816, 3613968, 7642004, 16313856, 35052905, 75487110, 162349105, 348018300, 743376838, 1583718457, 3370144462, 7173308802, 15285181447

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn
• easy

Comments

Number of compositions of 6*n-5 into parts 5 and 6.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,7,-1).

Crossrefs

Cf. A095263, A290998, A368475.

Cf. A000389, A099242, A017837, A107025.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/(1-x^5/(1-x)^6))

Formula

a(n) = A107025(n)-A107025(n-1). First differences of A107025.

a(n) = A017837(6*n-5) = Sum_{k=0..floor((6*n-5)/5)} binomial(k,6*n-5-5*k) for n > 0.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6) for n > 6.

a(n) = Sum_{k=0..floor(n/5)} binomial(n-1+k,n-5*k).