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%I #18 Apr 06 2021 08:07:06
%S 0,1,2,3,4,5,6,7,8,9,1,3,5,7,9,11,13,15,17,19,2,5,8,11,14,17,20,23,26,
%T 29,3,7,11,15,19,23,27,31,35,39,4,9,14,19,24,29,34,39,44,49,5,11,17,
%U 23,29,35,41,47,53,59,6,13,20,27,34,41,48,55,62,69,7,15,23,31,39,47,55,63,71,79,8,17,26,35,44,53,62,71,80,89,9,19,29,39,49,59,69,79,89,99,1,3
%N Let the number of digits in n be k; a(n) = sum of the products of the digits of n taken r at a time where r ranges from 1 to k.
%C Differs from A264600 first at n=101: a(101) = 3 != A264600(101) = 12. - _Alois P. Heinz_, Nov 20 2015
%H Alois P. Heinz, <a href="/A061486/b061486.txt">Table of n, a(n) for n = 0..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SymmetricPolynomial.html">Symmetric polynomial</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Elementary_symmetric_polynomial">Elementary symmetric polynomial</a>.
%e a(34) = 3 + 4 + 3*4 = 19, a(124) = (1+2+4)+(1*2+2*4+1*4)+(1*2*4) = 29.
%p with(combinat):
%p a:= n-> (l-> add(mul(l[i], i=w), w=choose(
%p nops(l)))-1)(convert(n, base, 10)):
%p seq(a(n), n=0..101); # _Alois P. Heinz_, Nov 20 2015
%o (PARI) sympol(X, n)=my(s=0); forvec(i=vector(n, j, [1, #X]), s+=prod(k=1, n, X[i[k]]), 2); s ;
%o a(n) = my(d=digits(n)); sum(k=1, #d, sympol(d, k)); \\ _Michel Marcus_, Apr 06 2021
%Y Cf. A264600, A264668.
%K nonn,base,look,easy
%O 0,3
%A _Amarnath Murthy_, May 06 2001
%E More terms from _Erich Friedman_, Jun 03 2001
%E a(0)=0 prepended by _Alois P. Heinz_, Nov 20 2015
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