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A239519 a(n) = n + (n-1)*(n-2) + (n-3)*(n-4)*(n-5) + (n-6)*(n-7)*(n-8)*(n-9) + ... + ...*1.

%I A239519 #13 Jun 25 2025 14:59:47
%S A239519 0,1,3,5,11,19,32,62,112,191,316,558,988,1711,2864,4661,7703,12883,
%T A239519 21626,35989,58826,94217,150017,239047,382676,614425,984452,1565021,
%U A239519 2458810,3826746,5918938,9136603,14115710,21842345,33804340,52186061,80128082,122221802
%N A239519 a(n) = n + (n-1)*(n-2) + (n-3)*(n-4)*(n-5) + (n-6)*(n-7)*(n-8)*(n-9) + ... + ...*1.
%C A239519 In other words, write n,n-1,n-2,...,n-k,...,1 and place '+' before the terms n-k, where k is triangular, place '*' elsewhere, then a(n) = result. - _Ralf Stephan_, Mar 29 2014
%e A239519 a(2) = 2 + 1 = 3.
%e A239519 a(3) = 3 + 2*1 = 5.
%e A239519 a(9) = 9 + 8*7 + 6*5*4 + 3*2*1 = 191.
%e A239519 a(10) = 10 + 9*8 + 7*6*5 + 4*3*2*1 = 316.
%o A239519 (Python)
%o A239519 for n in range(55):
%o A239519   sum_ = i = 0
%o A239519   k = 1
%o A239519   while i<n:
%o A239519     product = 1
%o A239519     for x in range(k):
%o A239519       product *= n - i
%o A239519       i += 1
%o A239519       if i>=n:  break
%o A239519     sum_ += product
%o A239519     k += 1
%o A239519   print(sum_, end=', ')
%Y A239519 Cf. A227363-A227367.
%K A239519 nonn
%O A239519 0,3
%A A239519 _Alex Ratushnyak_, Mar 20 2014