A160977 Number of partitions of n where every part appears at least 7 times.

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 3, 5, 4, 5, 6, 8, 7, 9, 9, 11, 11, 12, 15, 16, 16, 17, 19, 22, 21, 26, 26, 30, 31, 34, 36, 43, 46, 50, 52, 60, 62, 70, 74, 89, 88, 99, 104, 118, 122, 136, 150, 163, 169, 187, 196, 216, 227, 256, 264, 295, 304, 332, 350, 382, 411, 441

Offset

0,15

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..1000 from R. H. Hardin)

Formula

a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-7*x)) dx = -1.104868234083422137620242346741601264555358762045898765433... . - Vaclav Kotesovec, Jan 05 2016

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+add(b(n-i*j, i-1), j=7..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..78);  # Alois P. Heinz, Feb 06 2024

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(7*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

Crossrefs

Sequence in context: A161082 A161298 A161273 * A366931 A331541 A030738

Adjacent sequences: A160974 A160975 A160976 * A160978 A160979 A160980

Keyword

nonn

Author

R. H. Hardin, Jun 01 2009

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 06 2024

Status

approved