%I #21 Feb 16 2020 20:42:37
%S 0,1,5,35,70,210,330,715,1001,1820,2380,3876,4845,7315,8855,12650,
%T 14950,20475,23751,31465,35960,46376,52360,66045,73815,91390,101270,
%U 123410,135751,163185,178365,211876,230300,270725,292825,341055,367290,424270
%N List of numbers that are both pentagonal (A000326) and binomial coefficients C(n,4) (A000332).
%C All binomial coefficients C(n,4) belong to the generalized pentagonal sequence (A001318).
%C Pentagonal numbers of generalized pentagonal number (A001318) index number. - _Raphie Frank_, Nov 25 2012
%H William A. Tedeschi, <a href="/A145920/b145920.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentatopeNumber.html">Pentatope Number</a>.
%F a(n+1) = A000326 (A001318(n)).
%F Positive values of A000332(n) belong to the sequence if and only if 3 does not divide n. A000332(n) is positive when n>3.
%F Conjecture: a(n) = a(n-1) + 4a(n-2) - 4a(n-3) - 6a(n-4) + 6a(n-5) + 4a(n-6) - 4a(n-7) - a(n-8) + a(n-9). - _R. J. Mathar_, Oct 29 2008
%F Conjecture: G.f.: x^2(1 + 4x + 26x^2 + 19x^3 + 4x^5 + x^6 + 26x^4)/((1+x)^4(1-x)^5). - _R. J. Mathar_, Oct 29 2008
%F a(n) = (27x^4 - 18x^3 - 3x^2 + 2x)/8 where x = floor(n/2)*(-1)^n, for n >= 1. - _William A. Tedeschi_, Aug 16 2010
%e 35, for example, is both A000326(5) and A000332(7).
%Y Cf. A141919, of which this is a subsequence.
%K easy,nonn
%O 1,3
%A _Matthew Vandermast_, Oct 28 2008