A261740 Number of partitions of n where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order.

1, 6, 57, 398, 2955, 19158, 130453, 820554, 5280204, 32711022, 204324819, 1249546656, 7682267669, 46625705988, 283766862009, 1714704081724, 10374896682273, 62511439251768, 376943252871343, 2267304042230202, 13643684237963994, 81983795625450144

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ c * 6^n, where c = Product_{k>=2} 1/(1 - binomial(k+5,5)/6^k) = 3.760725122262068858184072984846959348360490081749654779894152320389687335... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021

G.f.: Product_{k>=1} 1 / (1 - binomial(k+5,5)*x^k). - Ilya Gutkovskiy, May 09 2021

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+5, 5))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Crossrefs

Column k=6 of A261718.

Sequence in context: A227813 A221575 A001593 * A296027 A229280 A124546

Adjacent sequences: A261737 A261738 A261739 * A261741 A261742 A261743

Keyword

nonn

Author

Alois P. Heinz, Aug 30 2015

Status

approved