0,3

Coefficient of x^n in ((1-x^10)/((1-x^5)(1-x^2)(1-x)))^n. - Michael Somos, Sep 24 2003

Note that n divides a(n+1)-a(n). - T. D. Noe (noe(AT)sspectra.com), Mar 16 2005

Terms that are not a multiple of 5 have zero density, namely, there are fewer than n^(log(4)/log(5)) such terms among A005191(1..n). In particular, A005191(5k+2) and A005191(5k+4) are multiples of 5 for every k. - Max Alekseyev (maxale(AT)gmail.com), Apr 25 2005

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

V. E. Hoggatt, Jr. and M. Bicknell, Diagonal sums of generalized Pascal triangles, Fib. Quart., 7 (1969), 341-358, 393.

T. D. Noe, Table of n, a(n) for n=0..200

a(n) = sum(k=0..[2n/5], binomial(n, k)*binomial(-n, 2n-5k) ); a(n) = (5^n + sum(j=1..2n-1, (sin(5j*Pi/(2n))/sin(j*Pi/(2n)))^n))/(2n) - 2. - Max Alekseyev (maxale(AT)gmail.com), Mar 04 2005

(PARI) a(n)=if(n<0, 0, polcoeff(((1-x^5)/(1-x)+x*O(x^(2*n)))^n, 2*n))

(PARI) a(n)=if(n<0, 0, polcoeff(((1-x^10)/((1-x^5)*(1-x^2)*(1-x))+x*O(x^n))^n, n))

(PARI) a(n) = sum(k=0, (2*n)\5, binomial(n, k)*binomial(-n, 2*n-5*k)) a(n) = round((5^n+sum(j=1, 2*n-1, (sin(5*Pi*j/2/n)/sin(Pi*j/2/n))^n))/2/n)-2 (Alekseyev)

Cf. A001405, A002426, A005190, A018901, A025012, A025013, A025014

Sequence in context: A149794 A149795 A149796 this_sequence A147091 A149797 A149798

Adjacent sequences: A005188 A005189 A005190 this_sequence A005192 A005193 A005194

nonn

N. J. A. Sloane (njas(AT)research.att.com).