A249345 The exponent of the highest power of 5 dividing the product of the elements on the n-th row of Pascal's triangle.

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

Offset

0,6

Links

Antti Karttunen, Table of n, a(n) for n = 0..3124

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.

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

Sequence in context: A071692 A307335 A030586 * A070635 A110366 A284801

Adjacent sequences: A249342 A249343 A249344 * A249346 A249347 A249348

Keyword

nonn

Author

Antti Karttunen, Oct 28 2014

Status

approved