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A078506 Decimal expansion of sum of inverses of unrestricted partition function. 5

%I

%S 2,5,1,0,5,9,7,4,8,3,8,8,6,2,9,3,9,5,3,2,3,6,8,3,4,7,2,7,4,1,5,4,6,5,

%T 4,5,1,6,8,3,5,3,1,9,4,4,9,5,5,1,4,7,6,8,1,9,0,8,0,6,2,9,9,6,5,0,8,3,

%U 8,4,5,3,2,9,0,4,4,6,1,8,4,2,3,8,1,9,2,5,8,7,1,4,6,2,8,2,7,8,0,9

%N Decimal expansion of sum of inverses of unrestricted partition function.

%C One could just as well sum from n >= 0, giving a value one higher. - _Franklin T. Adams-Watters_, Nov 30 2018

%H Vaclav Kotesovec, <a href="/A078506/b078506.txt">Table of n, a(n) for n = 1..1000</a>

%F Sum_{n>=1} 1/A000041(n) = 2.510597483886...

%e 2.510597483886293953236834727415465451683531944955147681908...

%t digits = 100; NSum[1/PartitionsP[n], {n, 1, Infinity}, NSumTerms -> 10000, WorkingPrecision -> digits+1] // RealDigits[#, 10, digits]& // First (* _Jean-Fran├žois Alcover_, Feb 21 2014 *)

%o (PARI)

%o default(realprecision,100);

%o N=10000; x='x+O('x^N);

%o v=Vec(Ser( 1/eta(x) ) );

%o s=sum(n=2,#v, 1.0/v[n] )

%o (PARI) {a(n) = if( n<-1, 0, n++; default( realprecision, n+5); floor( suminf( k=1, 1 / numbpart(k)) * 10^n) % 10)} /* _Michael Somos_, Feb 05 2011 */

%Y Cf. A000041, A237515, A303662.

%K cons,nonn

%O 1,1

%A _Ralf Stephan_, Jan 05 2003

%E Corrected digits from position 32 on by _Ralf Stephan_, Jan 24 2011

%E More terms from _Jean-Fran├žois Alcover_, Feb 21 2014

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)