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A246937
Number of partitions of n into 5 sorts of parts.
4
1, 5, 30, 155, 805, 4055, 20455, 102455, 513230, 2567230, 12841130, 64211380, 321082905, 1605444405, 8027354055, 40136925680, 200685295955, 1003427268205, 5017139711105, 25085702537730, 125428529603755, 627142668099880, 3135713425289030, 15678567227192655
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{i>=1} 1/(1-5*x^i).
a(n) ~ c * 5^n, where c = Product_{k>=1} 1/(1-1/5^k) = 1.3152135557353452193080... . - Vaclav Kotesovec, Mar 19 2015
G.f.: Sum_{i>=0} 5^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, 5*b(n-i, i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25);
MATHEMATICA
(O[x]^20 - 4/QPochhammer[5, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, 5 b[n-i, i]]]];
a[n_] := b[n, n];
a /@ Range[0, 25] (* Jean-François Alcover, Jan 02 2021, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A246935.
Sequence in context: A344064 A055298 A104891 * A110155 A122995 A254944
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 08 2014
STATUS
approved