A140952 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^11)).

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 13, 15, 17, 19, 22, 25, 28, 31, 35, 39, 43, 48, 53, 58, 64, 70, 77, 84, 91, 100, 108, 117, 127, 137, 148, 159, 172, 184, 198, 212, 227, 243, 259, 277, 295, 314, 334, 355, 377, 400, 424, 449, 475, 502, 531, 560

Offset: 0

Author

Alois P. Heinz, Jul 25 2008

Keywords

• nonn
• easy

Comments

Number of partitions of n into the first 5 primes.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,0,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,1,0,0,0,0,-1,-1,0,1).

Crossrefs

Cf. A000040, A025795, A029144, A103221, A140953, A335106.

Programs

Maple

M := Matrix(28, (i,j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 11, 15, 19, 20, 28])) then 1 elif j=1 and member(i, [8, 9, 13, 17, 25, 26]) then -1 else 0 fi):
a:= n-> (M^(n))[1,1]:
seq(a(n), n=0..50);

Mathematica

CoefficientList[Series[1/Times@@(1-x^Prime[Range[5]]),{x,0,70}],x] (* or *) LinearRecurrence[{0,1,1,0,0,0,0,-1,-1,0,1,0,-1,0,1,0,-1,0,1,1,0,0,0,0,-1,-1,0,1},{1,0,1,1,1,2,2,3,3,4,5,6,7,8,10,11,13,15,17,19,22,25,28,31,35,39,43,48},70] (* Harvey P. Dale, Jun 18 2021 *)