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a(n) = binomial(a,b) where a>=b and one of a and b is the product of the nonzero decimal digits of n and the other is the sum of the decimal digits of n.
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%I #18 Dec 16 2023 16:59:35

%S 1,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,1,3,1,6,28,120,495,2002,

%T 8008,31824,1,4,6,84,792,6435,48620,352716,2496144,17383860,1,5,28,

%U 792,12870,167960,1961256,21474180,225792840,2310789600,1,6,120,6435

%N a(n) = binomial(a,b) where a>=b and one of a and b is the product of the nonzero decimal digits of n and the other is the sum of the decimal digits of n.

%C Terms from _Robert G. Wilson v_.

%H Vincenzo Librandi, <a href="/A067453/b067453.txt">Table of n, a(n) for n = 0..1000</a> [Corrected by _Sean A. Irvine_, Dec 16 2023]

%t a = {}; Do[p = Apply[Times, IntegerDigits[n]]; s = Apply[Plus, IntegerDigits[n]]; a = Append[a, Binomial[Max[p, s], Min[p, s]]], {n, 0, 60}]; a (* _Robert G. Wilson v_ *)

%t bin[n_]:=Module[{idn=IntegerDigits[n],a,b},a=Times@@(idn/.{0->1});b= Total[ idn];If[a>b,Binomial[a,b],Binomial[b,a]]]; Array[bin,60] (* _Harvey P. Dale_, Apr 23 2014 *)

%K base,easy,nonn

%O 0,12

%A _Amarnath Murthy_, Feb 05 2002

%E Definition corrected by _Harvey P. Dale_, Apr 23 2014

%E Missing a(0)=1 inserted by _Sean A. Irvine_, Dec 16 2023