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A135852 A007318 * A103516 as a lower triangular matrix. 3
1, 3, 2, 8, 4, 3, 20, 6, 9, 4, 48, 8, 18, 16, 5, 112, 10, 30, 40, 25, 6, 256, 12, 45, 80, 75, 36, 7, 576, 14, 63, 140, 175, 126, 49, 8, 1280, 16, 84, 224, 350, 336, 196, 64, 9, 2816, 18, 108, 336, 630, 756, 588, 288, 81, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Binomial transform of triangle A103516.
LINKS
FORMULA
T(n, k) = (A007318 * A103516)(n, k).
T(n, 0) = A001792(n).
Sum_{k=0..n} T(n, k) = A099035(n+1).
T(n, k) = (k+1)*binomial(n, k), with T(n, 0) = (n+2)*2^(n-1), T(n, n) = n+1. - G. C. Greubel, Dec 07 2016
EXAMPLE
First few rows of the triangle are:
1;
3, 2;
8, 4, 3;
20, 6, 9, 4;
48, 8, 18, 16, 5;
112, 10, 30, 40, 25, 6;
256, 12, 45, 80, 75, 36, 7;
...
MATHEMATICA
T[n_, k_]:= If[n==0, 1, If[k==0, (n+2)*2^(n-1), (k+1)*Binomial[n, k]]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Dec 07 2016 *)
PROG
(Sage)
def A135852(n, k):
if (n==0): return 1
elif (k==0): return (n+2)*2^(n-1)
else: return (k+1)*binomial(n, k)
flatten([[A135852(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 07 2022
CROSSREFS
Cf. A001792 (1st column), A099035 (row sums).
Sequence in context: A344577 A019666 A110938 * A191731 A143515 A082333
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Dec 01 2007
EXTENSIONS
Offset changed to 0 by G. C. Greubel, Feb 07 2022
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)