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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 23 23:05 EDT 2021. Contains 348217 sequences. (Running on oeis4.)