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A129915 Irregular triangle read by rows: T(n, k) = f(n, A113474(n-1) - k), where f(n, k) = (n-1)!/2^k if (n-1)!/2^k is an integer, otherwise f(n, k) = 0.

%I A129915 #11 Sep 29 2024 13:18:21
%S A129915 1,1,1,2,3,6,3,6,12,24,15,30,60,120,45,90,180,360,720,315,630,1260,
%T A129915 2520,5040,315,630,1260,2520,5040,10080,20160,40320,2835,5670,11340,
%U A129915 22680,45360,90720,181440,362880,14175,28350,56700,113400,226800,453600
%N A129915 Irregular triangle read by rows: T(n, k) = f(n, A113474(n-1) - k), where f(n, k) = (n-1)!/2^k if (n-1)!/2^k is an integer, otherwise f(n, k) = 0.
%H A129915 G. C. Greubel, <a href="/A129915/b129915.txt">Rows n = 0..50 of the irregular triangle, flattened</a>
%F A129915 T(n, k) = f(n, A113474(n-1) - k), where f(n, k) = (n-1)!/2^k if (n-1)!/2^k is an integer, otherwise f(n, k) = 0, for n >= 1, 1 <= k <= A113474(n-1).
%e A129915 Irregular triangle begins as:
%e A129915     1;
%e A129915     1;
%e A129915     1,   2;
%e A129915     3,   6;
%e A129915     3,   6,   12,   24;
%e A129915    15,  30,   60,  120;
%e A129915    45,  90,  180,  360,  720;
%e A129915   315, 630, 1260, 2520, 5040;
%e A129915   315, 630, 1260, 2520, 5040, 10080, 20160, 40320;
%t A129915 A113474[n_]:= n+1 - DigitCount[n, 2, 1];
%t A129915 f[n_, k_]:= If[IntegerQ[(n-1)!/2^k], (n-1)!/2^k, 0];
%t A129915 A129915[n_, k_]:= f[n, A113474[n-1]-k];
%t A129915 Table[A129915[n,k], {n,15}, {k,A113474[n-1]}]//Flatten (* modified by _G. C. Greubel_, Sep 28 2024 *)
%o A129915 (Magma)
%o A129915 A113474:= func< n | n+1 - Multiplicity(Intseq(n, 2), 1) >;
%o A129915 f:= func< n,k | IsIntegral(Factorial(n-1)/2^k) select Factorial(n-1)/2^k else 0 >;
%o A129915 A129915:= func< n,k | f(n, A113474(n-1) - k) >;
%o A129915 [A129915(n,k): k in [1..A113474(n-1)], n in [1..12]]; // _G. C. Greubel_, Sep 28 2024
%o A129915 (SageMath)
%o A129915 def A113474(n): return n+1 - sum((n+0).digits(2))
%o A129915 def f(n,k): return factorial(n-1)/2^k if (factorial(n-1)/2^k).is_integer() else 0
%o A129915 def A129915(n,k): return f(n, A113474(n-1) - k)
%o A129915 flatten([[A129915(n,k) for k in range(1, A113474(n-1)+1)] for n in range(1,16)]) # _G. C. Greubel_, Sep 28 2024
%Y A129915 Cf. A049606, A067655, A113474.
%K A129915 nonn,tabf
%O A129915 1,4
%A A129915 _Roger L. Bagula_, Jun 05 2007
%E A129915 Edited by _G. C. Greubel_, Sep 28 2024