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A135853
A103516 * A007318 as an infinite lower triangular matrix.
3
1, 4, 2, 6, 6, 3, 8, 12, 12, 4, 10, 20, 30, 20, 5, 12, 30, 60, 60, 30, 6, 14, 42, 105, 140, 105, 42, 7, 16, 56, 168, 280, 280, 168, 56, 8, 18, 72, 252, 504, 630, 504, 252, 72, 9, 20, 90, 360, 840, 1260, 1260, 840, 360, 90, 10
OFFSET
0,2
FORMULA
T(n, k) = (A103516 * A007318)(n, k).
Sum_{k=0..n} T(n, k) = A135854(n).
T(n, k) = (k+1)*binomial(n+1, k+1), with T(n, n) = n+1, T(n, 0) = 2*(n+1). - G. C. Greubel, Dec 07 2016
T(n, 0) = A103517(n). - G. C. Greubel, Feb 06 2022
EXAMPLE
First few rows of the triangle are:
1;
4, 2;
6, 6, 3;
8, 12, 12, 4;
10, 20, 30, 20, 5;
12, 30, 60, 60, 30, 6;
14, 42, 105, 140, 105, 42, 7;
...
MATHEMATICA
T[n_, k_]:= If[k==n, n+1, If[k==0, 2*(n+1), (k+1)*Binomial[n+1, k+1]]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//flatten (* G. C. Greubel, Dec 07 2016 *)
PROG
(Sage)
def A135853(n, k):
if (n==0): return 1
elif (k==0): return 2*(n+1)
else: return (k+1)*binomial(n+1, k+1)
flatten([[A135853(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 06 2022
CROSSREFS
Cf. A103517 (1st column), A135854 (row sums).
Sequence in context: A344123 A188941 A200347 * A376240 A338915 A173197
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Dec 01 2007
STATUS
approved