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 A182737 Sum of parts in all partitions of 2n+1 that do not contain 1 as a part. 3

%I

%S 0,3,10,28,72,154,312,615,1122,1995,3465,5819,9575,15498,24563,38378,

%T 59202,90055,135420,201630,297045,433741,628155,902212,1286348,

%U 1821567,2562126,3581655,4977867,6879400,9457318,12936609,17610320,23863323,32196090

%N Sum of parts in all partitions of 2n+1 that do not contain 1 as a part.

%C Bisection (odd part) of A138880.

%H Alois P. Heinz, <a href="/A182737/b182737.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A005408(n)*A182747(n).

%p b:= proc(n,i) option remember; local p,q;

%p if n<0 then [0,0]

%p elif n=0 then [1,0]

%p elif i<2 then [0,0]

%p else p, q:= b(n,i-1), b(n-i,i);

%p [p[1]+q[1], p[2]+q[2]+q[1]*i]

%p fi

%p end:

%p a:= n-> b(2*n+1,2*n+1)[2]:

%p seq(a(n), n=0..34); # _Alois P. Heinz_, Dec 03 2010

%t b[n_, i_] := b[n, i] = Module[{p, q}, Which[n<0, {0, 0}, n == 0, {1, 0}, i<2, {0, 0}, True, {p, q} = {b[n, i-1], b[n-i, i]}; {p[[1]] + q[[1]], p[[2]] + q[[2]] + q[[1]]*i}]]; a[n_] := b[2*n + 1, 2*n+1][[2]]; Table[ a[n], {n, 0, 34}] (* _Jean-François Alcover_, Nov 11 2015, after _Alois P. Heinz_ *)

%Y Cf. A135010, A138121, A138880, A182736, A182743.

%K nonn

%O 0,2

%A _Omar E. Pol_, Dec 03 2010

%E More terms from _Alois P. Heinz_, Dec 03 2010

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Last modified June 20 13:08 EDT 2021. Contains 345164 sequences. (Running on oeis4.)