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a(n) = C(n,a)+C(n,b)+C(n,c)... where n = abc... are the decimal digits of n.
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%I #5 Dec 05 2013 19:57:05

%S 1,1,1,1,1,1,1,1,1,1,11,22,78,299,1015,3018,8024,19465,43776,92397,

%T 191,231,462,2024,10902,53430,230555,888381,3108483,10015411,4061,

%U 4526,5456,10912,52360,331177,1954932,10303242,48911928,211924271,91391,101311

%N a(n) = C(n,a)+C(n,b)+C(n,c)... where n = abc... are the decimal digits of n.

%C a(10^n) = 10^n. a{(10^n-1)/9} = n*((10^n-1)/9).

%C a(0)=1 since C(0,0)=1.

%e a(12) = C(12,1)+C(12,2) = 12+66 = 78.

%e a(111) = 333.

%t f[n_] := Plus @@ Binomial[n, IntegerDigits[n]]; Table[ f[n], {n, 41}] (* _Robert G. Wilson v_ *)

%Y Cf. A111695.

%K base,easy,nonn

%O 0,11

%A _Amarnath Murthy_, Aug 17 2005

%E Edited, corrected and extended by _Robert G. Wilson v_, Aug 19 2005