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A308475 a(1) = 1; a(n) = Sum_{k=1..n-1, gcd(n,k) = 1} binomial(n,k)*a(k). 1
1, 2, 9, 40, 315, 1896, 21651, 191360, 2546487, 28064080, 488517183, 5879603280, 124673371719, 1928346159572, 42684093159480, 754925802649360, 20289814995554811, 366300418631427144, 11352374441063693655, 250187625076714423520, 7774760839170720287739 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..425

MAPLE

a:= proc(n) option remember;

if n=1 then 1;

else add( `if`(gcd(n, j)=1, binomial(n, j)*a(j), 0), j=1..n-1);

end if; end proc;

seq(a(n), n = 1..30); # G. C. Greubel, Mar 08 2021

MATHEMATICA

a[n_] := Sum[If[GCD[n, k] == 1, Binomial[n, k] a[k], 0], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 21}]

PROG

(Sage)

@CachedFunction

def a(n):

if n==1: return 1

else: return sum( kronecker_delta(gcd(n, j), 1)*binomial(n, j)*a(j) for j in (1..n-1) )

[a(n) for n in (1..30)] # G. C. Greubel, Mar 08 2021

CROSSREFS

Cf. A000670, A045545, A052882, A056188.

Sequence in context: A220471 A213095 A238372 * A002825 A259339 A346841

Adjacent sequences: A308472 A308473 A308474 * A308476 A308477 A308478

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 29 2019

STATUS

approved

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Last modified December 4 02:16 EST 2022. Contains 358544 sequences. (Running on oeis4.)