A341989 Number of ways to write n as an ordered sum of 10 primes (counting 1 as a prime).

1, 10, 55, 210, 625, 1542, 3310, 6390, 11400, 19090, 30353, 46060, 67210, 94780, 130230, 174862, 230650, 298800, 382115, 482090, 603373, 746860, 918770, 1118100, 1355110, 1626742, 1949190, 2312380, 2740220, 3212640, 3769784, 4375900, 5092485, 5854680, 6758935, 7703112

Offset: 10

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

• nonn

Crossrefs

Cf. A008578, A280917, A283762, A340966, A341972, A341981, A341982, A341983, A341984, A341985, A341986, A341987, A341988.

Programs

Maple

b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
      `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 11)
    end:
a:= n-> coeff(b(n), x, 10):
seq(a(n), n=10..45);  # Alois P. Heinz, Feb 25 2021

Mathematica

nmax = 45; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^10.