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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. 2
1, 5, 40, 235, 1470, 8001, 45865, 241870, 1307055, 6783210, 35510502, 181665635, 934801705, 4741017595, 24118500815, 121693135003, 614889556920, 3091596201560, 15557885702390, 78054925105630, 391798489621630, 1963104427709830, 9838685572501515 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 30 2015
STATUS
approved

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Last modified June 18 21:09 EDT 2024. Contains 373487 sequences. (Running on oeis4.)