OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 21 2013
STATUS
approved