A261741 Number of partitions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order.

1, 7, 77, 623, 5355, 40299, 317905, 2323483, 17353028, 124991685, 907465307, 6458846989, 46199021001, 326573565143, 2314422214435, 16296707707077, 114891467946017, 806991845455033, 5672334432498356, 39785054428093380, 279156880971492454, 1956352659297436368

Offset: 0

Author

Alois P. Heinz, Aug 30 2015

Keywords

• nonn

Links

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

Crossrefs

Column k=7 of A261718.

Programs

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+6, 6))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Formula

a(n) ~ c * 7^n, where c = Product_{k>=2} 1/(1 - binomial(k+6,6)/7^k) = 3.519268129363442517546929108933080435102442778133731795486515352... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021

G.f.: Product_{k>=1} 1 / (1 - binomial(k+6,6)*x^k). - Ilya Gutkovskiy, May 10 2021