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A172497 Triangle T(n, k) = round( c(n)/(c(k)*c(n-k)) ) where c(n) = Product_{j=1..n} A029826(j+10), read by rows. 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 4, 2, 2, 1, 1, 3, 6, 6, 6, 6, 3, 1, 1, 2, 6, 12, 6, 12, 6, 2, 1, 1, 4, 8, 24, 24, 24, 24, 8, 4, 1, 1, 3, 12, 24, 36, 72, 36, 24, 12, 3, 1, 1, 5, 15, 60, 60, 180, 180, 60, 60, 15, 5, 1, 1, 5, 25, 75, 150, 300, 450, 300, 150, 75, 25, 5, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,12
LINKS
FORMULA
T(n, k) = round( c(n)/(c(k)*c(n-k)) ) where c(n) = Product_{j=1..n} A029826(j+10).
EXAMPLE
The triangle begins as:
1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 2, 2, 2, 1;
1, 1, 2, 2, 1, 1;
1, 2, 2, 4, 2, 2, 1;
1, 3, 6, 6, 6, 6, 3, 1;
1, 2, 6, 12, 6, 12, 6, 2, 1;
1, 4, 8, 24, 24, 24, 24, 8, 4, 1;
1, 3, 12, 24, 36, 72, 36, 24, 12, 3, 1;
MATHEMATICA
b:= Drop[CoefficientList[Series[1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10), {x, 0, 100}], x], 10];
c[n_]:= Product[b[[j]], {j, n}];
T[n_, k_]:= Round[c[n]/(c[k]*c[n-k])];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 20 2021 *)
PROG
(Magma)
R<x>:= PowerSeriesRing(Integers(), 100);
b:= Coefficients(R!( 1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10) ));
c:= func< n | (&*[b[j]: j in [10..n+10]]) >;
T:= func< n, k | Round(c(n)/(c(k)*c(n-k))) >;
[T(n, k): k in [0..n], n in [1..12]]; // G. C. Greubel, Apr 20 2021
(Sage)
@CachedFunction
def A029826_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10) ).list()
b=A029826_list(130)
def c(n): return product(b[j] for j in (9..n+9))
def T(n, k): return round(c(n)/(c(k)*c(n-k)))
flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 20 2021
CROSSREFS
Cf. A029826.
Sequence in context: A238408 A048858 A246465 * A211226 A306366 A135265
KEYWORD
nonn,tabl,easy,less
AUTHOR
Roger L. Bagula, Feb 05 2010
EXTENSIONS
Definition corrected and edited by G. C. Greubel, Apr 20 2021
STATUS
approved

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Last modified July 20 05:10 EDT 2024. Contains 374441 sequences. (Running on oeis4.)