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A218394 Numbers such that sum(i<=n) binomial(n,i)*binomial(2*n-2*i, n-i) is not divisible by 5. 0
1, 5, 7, 11, 25, 27, 31, 35, 37, 51, 55, 57, 61, 125, 127, 131, 135, 137, 151, 155, 157, 161, 175, 177, 181, 185, 187, 251, 255, 257, 261, 275, 277, 281, 285, 287, 301, 305, 307, 311, 625, 627, 631, 635, 637, 651, 655, 657, 661, 675, 677, 681, 685, 687, 751 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = A037453(2*n-1) (proved by Schur, see link).

LINKS

Table of n, a(n) for n=1..55.

W. Shur, The last digit of C(2*n,n) and Sigma C(n,i)*C(2*n-2*i,n-i), The Electronic Journal of Combinatorics, #R16, Volume 4, Issue 2 (1997).

FORMULA

a(n)=2*n - 1 + 2*sum{i=1,n} 5^(i-1)*floor((2*n-1)/3^i).

PROG

(PARI) a(nb) = {for (n=1, nb, if (sum(i=1, n, binomial(n, i)*binomial(2*n-2*i, n-i)) % 5 != 0, print1(n, ", ")); ); }

(PARI) a(n) = {2*n-1+2*sum(i=1, n, 5^(i-1)*floor((2*n-1)/3^i))}

CROSSREFS

Cf. A037453.

Sequence in context: A181602 A075705 A249735 * A067289 A036491 A036490

Adjacent sequences:  A218391 A218392 A218393 * A218395 A218396 A218397

KEYWORD

nonn

AUTHOR

Michel Marcus, Oct 28 2012

STATUS

approved

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Last modified February 16 18:53 EST 2019. Contains 320165 sequences. (Running on oeis4.)