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A226875
Number of n-length words w over a 5-ary alphabet {a1,a2,...,a5} such that #(w,a1) >= #(w,a2) >= ... >= #(w,a5) >= 0, where #(w,x) counts the letters x in word w.
4
1, 1, 3, 10, 47, 246, 882, 3921, 18223, 84790, 432518, 1863951, 8892842, 42656147, 204204353, 1025014815, 4728033983, 22948258742, 111605089014, 541696830843, 2708218059022, 12861557284425, 62938669549583, 308273057334413, 1508708926286914, 7533652902408071
OFFSET
0,3
LINKS
FORMULA
Conjecture: a(n) ~ 5^n/5!. - Vaclav Kotesovec, Mar 07 2014
MAPLE
b:= proc(n, i, t) option remember;
`if`(t=1, 1/n!, add(b(n-j, j, t-1)/j!, j=i..n/t))
end:
a:= n-> n!*b(n, 0, 5):
seq(a(n), n=0..30);
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[If[i+j+k+l+m==n, n!/i!/j!/k!/l!/m!, 0], {m, 0, l}], {l, 0, k}], {k, 0, j}], {j, 0, i}], {i, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 01 2013 *)
CoefficientList[Series[(HypergeometricPFQ[{}, {}, x]^5 + 10*HypergeometricPFQ[{}, {}, x]^3*HypergeometricPFQ[{}, {1}, x^2] + 20*HypergeometricPFQ[{}, {}, x]^2*HypergeometricPFQ[{}, {1, 1}, x^3] + 20*HypergeometricPFQ[{}, {1}, x^2]*HypergeometricPFQ[{}, {1, 1}, x^3] + 15*HypergeometricPFQ[{}, {1}, x^2]^2*HypergeometricPFQ[{}, {}, x] + 30*HypergeometricPFQ[{}, {1, 1, 1}, x^4]*HypergeometricPFQ[{}, {}, x] + 24*HypergeometricPFQ[{}, {1, 1, 1, 1}, x^5])/5!, {x, 0, 20}], x]*Range[0, 20]! (* more efficient, Vaclav Kotesovec, Jul 01 2013 *)
CROSSREFS
Column k=5 of A226873.
Sequence in context: A092429 A218919 A346188 * A226876 A325308 A226877
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 21 2013
STATUS
approved