A249345 - OEIS

%I #18 Jul 22 2022 10:47:31

%S 0,0,0,0,0,4,3,2,1,0,8,6,4,2,0,12,9,6,3,0,16,12,8,4,0,44,38,32,26,20,

%T 43,36,29,22,15,42,34,26,18,10,41,32,23,14,5,40,30,20,10,0,88,76,64,

%U 52,40,82,69,56,43,30,76,62,48,34,20,70,55,40,25,10,64,48,32,16,0

%N The exponent of the highest power of 5 dividing the product of the elements on the n-th row of Pascal's triangle.

%H Antti Karttunen, <a href="/A249345/b249345.txt">Table of n, a(n) for n = 0..3124</a>

%H Jeffrey C. Lagarias and Harsh Mehta, <a href="http://arxiv.org/abs/1409.4145">Products of binomial coefficients and unreduced Farey fractions</a>, arXiv:1409.4145 [math.NT], 2014.

%F a(n) = A112765(A001142(n)).

%F a(n) = Sum_{k=0..n} A112765(binomial(n,k)).

%F a(n) = Sum_{i=1..n} (2*i-n-1)*v_5(i), where v_5(i) = A112765(i) is the exponent of the highest power of 5 dividing i. - _Ridouane Oudra_, Jun 02 2022

%o (PARI)

%o allocatemem(234567890);

%o A249345(n) = sum(k=0, n, valuation(binomial(n, k), 5));

%o for(n=0, 3124, write("b249345.txt", n, " ", A249345(n)));

%o (Scheme, two alternative definitions)

%o (define (A249345 n) (A112765 (A001142 n)))

%o (define (A249345 n) (add (lambda (n) (A112765 (A007318 n))) (A000217 n) (A000096 n)))

%o (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))

%Y Row 3 of array A249421.

%Y Cf. A001142, A007318, A112765, A187059, A249343, A249347.

%K nonn

%O 0,6

%A _Antti Karttunen_, Oct 28 2014