A143963 Binomial transform of A012245 (characteristic function of factorial numbers).

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

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Cf. A007318, A012245.

Sequence in context: A226239 A209231 A137358 * A139714 A342211 A262927

Adjacent sequences: A143960 A143961 A143962 * A143964 A143965 A143966

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2008

Status

approved