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A293369
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 and all five letters occur at least once in the partition.
2
246, 4350, 44475, 369675, 2603670, 16993932, 102603315, 598010585, 3339393990, 18294499370, 97818690363, 517148440820, 2694756962105, 13947673300505, 71555207694490, 365571598248050, 1857609632705200, 9414446265923035, 47553294423090160, 239799029393392505
OFFSET
5,1
LINKS
FORMULA
a(n) ~ c * 5^n, where c = 4.1548340497015786311470026968208254860294132084317763408428889184148319... - Vaclav Kotesovec, Oct 11 2017
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))
end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(5):
seq(a(n), n=5..30);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, b[n - i, i, k] Binomial[i + k - 1, k - 1]]]];
a[n_] := With[{k = 5}, Sum[b[n, n, k-i] (-1)^i Binomial[k, i], {i, 0, k}]];
a /@ Range[5, 30] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A261719.
Sequence in context: A074995 A251524 A251517 * A212475 A186787 A229478
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 07 2017
STATUS
approved