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

0,2

Links

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

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

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);

Crossrefs

Column k=7 of A261718.

Sequence in context: A213261 A268958 A068667 * A228414 A043042 A191465

Adjacent sequences: A261738 A261739 A261740 * A261742 A261743 A261744

Keyword

nonn

Author

Alois P. Heinz, Aug 30 2015

Status

approved