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A246940
Number of partitions of n into 8 sorts of parts.
3
1, 8, 72, 584, 4744, 38024, 304840, 2439368, 19520264, 156167944, 1249386824, 9995142472, 79961491848, 639692324232, 5117541421512, 40940334536648, 327522698972168, 2620181617189384, 20961453119350856, 167691625158581832, 1341533002724164744
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{i>=1} 1/(1-8*x^i).
a(n) ~ c * 8^n, where c = Product_{k>=1} 1/(1-1/8^k) = 1.1635943971944701027405... . - Vaclav Kotesovec, Mar 19 2015
G.f.: Sum_{i>=0} 8^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 12 2018
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1) +`if`(i>n, 0, 8*b(n-i, i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25);
MATHEMATICA
(O[x]^20 - 7/QPochhammer[8, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)
CROSSREFS
Column k=8 of A246935.
Sequence in context: A344067 A111919 A052379 * A158798 A229249 A242160
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 08 2014
STATUS
approved