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A261737 Number of partitions of n where each part i is marked with a word of length i over a ternary alphabet whose letters appear in alphabetical order. 3
1, 3, 15, 55, 216, 729, 2621, 8535, 28689, 91749, 296538, 929712, 2939063, 9093255, 28257123, 86681608, 266368959, 811501848, 2475331535, 7505567037, 22772955015, 68828023329, 208079886258, 627418618533, 1892181244828, 5696253823476, 17149663331259 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) ~ c * 3^n, where c = Product_{k>=2} 1/(1 - (k+1)*(k+2)/(2*3^k)) = 6.84620607349852135789816336867607014231681538613599316638081993041973716978... . - Vaclav Kotesovec, Nov 15 2016, updated May 10 2021
G.f.: Product_{k>=1} 1 / (1 - binomial(k+2,2)*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+2, 2))))
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 + 2, 2]]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 30}] {* Jean-François Alcover, May 24 2018, translated from Maple *)
CROSSREFS
Column k=3 of A261718.
Cf. A293367.
Sequence in context: A286185 A152896 A007973 * A015249 A084152 A084175
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 30 2015
STATUS
approved

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Last modified June 16 12:15 EDT 2024. Contains 373429 sequences. (Running on oeis4.)