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A143963 Binomial transform of A012245 (characteristic function of factorial numbers). 1
0, 1, 3, 6, 10, 15, 22, 35, 64, 129, 265, 528, 1002, 1807, 3108, 5125, 8144, 12529, 18735, 27322, 38970, 54495, 74866, 101223, 134897, 177450, 230906, 299313, 397621, 594210, 1188015, 3366352, 11425020, 39675229, 132473639, 418849690, 1253626158, 3564792787 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=1..n} C(n,k)*A012245(k).
EXAMPLE
a(6) = [6,15,20,15,6,1]*[1,1,0,0,0,1] = 6+15+1 = 22.
MAPLE
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);
PROG
(Python)
from math import comb
def A143963(n):
c, i, s = 1, 1, 0
while (c:=c*i) <= n:
s += comb(n, c)
i += 1
return s # Chai Wah Wu, Jan 11 2023
CROSSREFS
Sequence in context: A226239 A209231 A137358 * A139714 A342211 A262927
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 05 2008
STATUS
approved

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Last modified April 17 11:20 EDT 2024. Contains 371763 sequences. (Running on oeis4.)