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%I #14 Jan 11 2023 11:45:52
%S 0,1,3,6,10,15,22,35,64,129,265,528,1002,1807,3108,5125,8144,12529,
%T 18735,27322,38970,54495,74866,101223,134897,177450,230906,299313,
%U 397621,594210,1188015,3366352,11425020,39675229,132473639,418849690,1253626158,3564792787
%N Binomial transform of A012245 (characteristic function of factorial numbers).
%H Alois P. Heinz, <a href="/A143963/b143963.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=1..n} C(n,k)*A012245(k).
%e a(6) = [6,15,20,15,6,1]*[1,1,0,0,0,1] = 6+15+1 = 22.
%p a:= proc(n) local k,i,s; s:=0; k:=1; i:=1; while k<=n do s:= s+ binomial(n,k); i:=i+1; k:=k*i; od; s; end: seq(a(n), n=0..40);
%o (Python)
%o from math import comb
%o def A143963(n):
%o c, i, s = 1, 1, 0
%o while (c:=c*i) <= n:
%o s += comb(n,c)
%o i += 1
%o return s # _Chai Wah Wu_, Jan 11 2023
%Y Cf. A007318, A012245.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 05 2008
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