A320377 Number of parts in all partitions of n with largest multiplicity seven.

7, 0, 8, 8, 17, 17, 36, 43, 74, 85, 136, 167, 254, 308, 437, 550, 754, 944, 1270, 1581, 2088, 2588, 3356, 4160, 5326, 6568, 8306, 10217, 12776, 15634, 19413, 23644, 29134, 35360, 43250, 52285, 63599, 76547, 92608, 111079, 133705, 159774, 191477, 228012, 272104

Offset

7,1

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

a(n) ~ 3^(5/4) * log(2) * exp(Pi*sqrt(7*n/3)/2) / (2^(3/2) * 7^(1/4) * Pi * n^(1/4)). - Vaclav Kotesovec, Oct 25 2018

Maple

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
    end:
a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(7):
seq(a(n), n=7..50);

Crossrefs

Column k=7 of A213177.

Sequence in context: A190410 A283881 A178308 * A213186 A296482 A272429

Adjacent sequences: A320374 A320375 A320376 * A320378 A320379 A320380

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2018

Status

approved