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.

246, 4350, 44475, 369675, 2603670, 16993932, 102603315, 598010585, 3339393990, 18294499370, 97818690363, 517148440820, 2694756962105, 13947673300505, 71555207694490, 365571598248050, 1857609632705200, 9414446265923035, 47553294423090160, 239799029393392505

Offset

5,1

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

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

Adjacent sequences: A293366 A293367 A293368 * A293370 A293371 A293372

Keyword

nonn

Author

Alois P. Heinz, Oct 07 2017

Status

approved