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A208656 Triangle T(n, k) = n*C(n,k) - C(n-1,k-1), 1 <= k <= n, read by rows. 2
0, 3, 1, 8, 7, 2, 15, 21, 13, 3, 24, 46, 44, 21, 4, 35, 85, 110, 80, 31, 5, 48, 141, 230, 225, 132, 43, 6, 63, 217, 427, 525, 413, 203, 57, 7, 80, 316, 728, 1078, 1064, 700, 296, 73, 8, 99, 441, 1164, 2016, 2394, 1974, 1116, 414, 91, 9, 120, 595, 1770 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Mirror of A208657.
col 1: A005563
col 2: A127736
top edge: A000027
LINKS
EXAMPLE
First five rows:
0
3....1
8....7....2
15...21...13...3
24...46...44...21...4
MATHEMATICA
z = 12;
f[n_, k_] := n*Binomial[n, k] - Binomial[n - 1, k - 1]
t = Table[f[n, k], {n, 1, z}, {k, 1, n}];
TableForm[t] (* A208656 as a triangle *)
Flatten[t] (* A208656 as a sequence *)
r = Table[f[n, k], {n, 1, z}, {k, n, 1, -1}];
TableForm[r] (* A208657 as a triangle *)
Flatten[r] (* A208657 as a sequence *)
Table[Sum[f[n, k], {k, 1, n}], {n, 1, 3 z}](* A208658 *)
CROSSREFS
Sequence in context: A308737 A257142 A270861 * A242440 A245651 A007023
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 01 2012
EXTENSIONS
Definition amended by Georg Fischer, Feb 01 2022
STATUS
approved

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Last modified April 15 15:27 EDT 2024. Contains 371692 sequences. (Running on oeis4.)