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A249345 The exponent of the highest power of 5 dividing the product of the elements on the n-th row of Pascal's triangle. 6
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, 43, 36, 29, 22, 15, 42, 34, 26, 18, 10, 41, 32, 23, 14, 5, 40, 30, 20, 10, 0, 88, 76, 64, 52, 40, 82, 69, 56, 43, 30, 76, 62, 48, 34, 20, 70, 55, 40, 25, 10, 64, 48, 32, 16, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
Jeffrey C. Lagarias and Harsh Mehta, Products of binomial coefficients and unreduced Farey fractions, arXiv:1409.4145 [math.NT], 2014.
FORMULA
a(n) = A112765(A001142(n)).
a(n) = Sum_{k=0..n} A112765(binomial(n,k)).
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
PROG
(PARI)
allocatemem(234567890);
A249345(n) = sum(k=0, n, valuation(binomial(n, k), 5));
for(n=0, 3124, write("b249345.txt", n, " ", A249345(n)));
(Scheme, two alternative definitions)
(define (A249345 n) (A112765 (A001142 n)))
(define (A249345 n) (add (lambda (n) (A112765 (A007318 n))) (A000217 n) (A000096 n)))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))
CROSSREFS
Row 3 of array A249421.
Sequence in context: A071692 A307335 A030586 * A070635 A110366 A284801
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 28 2014
STATUS
approved

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Last modified February 23 06:06 EST 2024. Contains 370267 sequences. (Running on oeis4.)