A261739 Number of partitions of n where each part i is marked with a word of length i over a quinary alphabet whose letters appear in alphabetical order.

1, 5, 40, 235, 1470, 8001, 45865, 241870, 1307055, 6783210, 35510502, 181665635, 934801705, 4741017595, 24118500815, 121693135003, 614889556920, 3091596201560, 15557885702390, 78054925105630, 391798489621630, 1963104427709830, 9838685572501515

Offset

0,2

Links

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

Formula

a(n) ~ c * 5^n, where c = Product_{k>=2} 1/(1 - (k+1)*(k+2)*(k+3)*(k+4)/(24*5^k)) = 4.1548340497015786311470026968208254860294132084317763408428889184148319... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021

G.f.: Product_{k>=1} 1 / (1 - binomial(k+4,4)*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+4, 4))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n, 0, b[n - i, i]*Binomial[i + 4, 4]]]];
a[n_] := b[n, n];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A261718.

Sequence in context: A271092 A273653 A081364 * A230744 A269822 A043019

Adjacent sequences: A261736 A261737 A261738 * A261740 A261741 A261742

Keyword

nonn

Author

Alois P. Heinz, Aug 30 2015

Status

approved