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A255767
Triangle read by rows: T(n,k) = sum of all parts of all partitions of n into k distinct parts.
2
1, 4, 6, 3, 12, 8, 10, 25, 24, 36, 6, 14, 77, 14, 32, 104, 40, 27, 153, 90, 40, 220, 150, 10, 22, 297, 275, 22, 72, 348, 444, 60, 26, 481, 676, 130, 56, 616, 938, 280, 60, 660, 1455, 450, 15, 80, 880, 1872, 832, 32, 34, 1003, 2618, 1309, 85, 108, 1224, 3312, 2106, 180, 38, 1349, 4465, 3078, 380, 120, 1620, 5540, 4540, 720
OFFSET
1,2
COMMENTS
Row n has length A003056(n) hence the first element of column k is in row A000217(n).
The first element of column k is A000217(k).
Column 1 is A038040.
LINKS
FORMULA
T(n,k) = n * A116608(n,k).
EXAMPLE
Triangle begins:
1;
4;
6, 3;
12, 8;
10, 25;
24, 36, 6;
14, 77, 14;
32, 104, 40;
27, 153, 90;
40, 220, 150, 10;
22, 297, 275, 22;
72, 348, 444, 60;
26, 481, 676, 130;
56, 616, 938, 280;
60, 660, 1455, 450, 15;
80, 880, 1872, 832, 32;
34, 1003, 2618, 1309, 85;
108, 1224, 3312, 2106, 180;
38, 1349, 4465, 3078, 380;
...
MAPLE
A255767 := proc(n, k)
n*A116608(n, k) ;
end proc:
for n from 1 to 20 do
for k from 1 to A003056(n) do
printf("%d, ", A255767(n, k)) ;
end do:
printf("\n") ;
end do: # R. J. Mathar, Jul 10 2015
# second Maple program:
b:= proc(n, i) option remember; local j; if n=0 then 1
elif i<1 then 0 else []; for j from 0 to n/i do zip((x, y)
->x+y, %, [`if`(j>0, 0, [][]), b(n-i*j, i-1)], 0) od; %[] fi
end:
T:= n-> subsop(1=NULL, n*[b(n, n)])[]:
seq(T(n), n=1..30); # Alois P. Heinz, Jul 26 2015
MATHEMATICA
nmax = 30; T = Rest[CoefficientList[#, t]]& /@ Rest[CoefficientList[-1 + Product[1 + t x^j/(1 - x^j), {j, 1, nmax}] + O[x]^(nmax+1), x]];
Table[n*T[[n]], {n, 1, nmax}] // Flatten (* Jean-François Alcover, May 19 2018 *)
CROSSREFS
Sequence in context: A198113 A264962 A082193 * A274926 A079171 A029678
KEYWORD
nonn,tabf,look
AUTHOR
Omar E. Pol, May 21 2015
EXTENSIONS
a(7) and beyond from R. J. Mathar, Jul 10 2015
STATUS
approved