A341226 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^7.

1, 14, 105, 567, 2478, 9317, 31269, 95965, 273896, 735966, 1879059, 4591342, 10797290, 24549924, 54171729, 116368308, 243991034, 500446135, 1006039762, 1985480063, 3852429483, 7358212272, 13850448185, 25718189483, 47150564517, 85417834621, 153015826880

Offset: 7

Author

Ilya Gutkovskiy, Feb 07 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..10000

Crossrefs

Column k=7 of A060642.

Cf. A000041, A023006, A048574, A327385, A341221, A341222, A341223, A341225, A341227, A341228.

Programs

Maple

b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, combinat[
      numbpart](n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
    end:
a:= n-> b(n, 7):
seq(a(n), n=7..33);  # Alois P. Heinz, Feb 07 2021

Mathematica

nmax = 33; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &