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A194552 Sum of all parts > 1 of all partitions of n. 4
0, 2, 5, 13, 23, 47, 75, 131, 203, 323, 477, 729, 1041, 1517, 2132, 3012, 4134, 5718, 7713, 10453, 13918, 18538, 24357, 32037, 41612, 54040, 69538, 89362, 113925, 145095, 183473, 231697, 290899, 364577, 454632, 566016, 701436, 867800, 1069430, 1315550, 1612595 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also the total number of missing parts in the partitions of n. A missing part of a partition of n is any number from 1 to n not occurring as a part. For example for n = 3, 1,2 are missing from 3; 3 is missing from 2+1, and 2,3 are missing from 1+1+1, for a total of a(3) = 5. - George Beck, Oct 23 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A066186(n) - A000070(n-1).

a(n) = n * A000041(n) - A000070(n-1). - George Beck, Oct 24 2014

G.f.: (x/(1 - x)) * (d/dx) Product_{k>=2} 1/(1 - x^k). - Ilya Gutkovskiy, Mar 06 2021

MAPLE

b:= proc(n, i) option remember; local h, t;

if n<0 or i<1 then [0, 0]

elif n=0 or i=1 then [1, 0]

else h:= b(n, i-1); t:= b(n-i, i);

[h[1]+t[1], h[2]+t[2] +t[1]*i]

fi

end:

a:= n-> b(n, n)[2]:

seq(a(n), n=1..50); # Alois P. Heinz, Dec 14 2011

MATHEMATICA

a[n_] := n PartitionsP[n] -Total@Table[PartitionsP[k], {k, 0, n - 1}]; a /@ Range[40] (* George Beck, Oct 23 2014 *)

CROSSREFS

Partial sums of A138880.

Cf. A096541, A135010, A138121, A138135.

Sequence in context: A281906 A256491 A106009 * A079780 A178621 A309230

Adjacent sequences: A194549 A194550 A194551 * A194553 A194554 A194555

KEYWORD

nonn

AUTHOR

Omar E. Pol, Dec 11 2011

STATUS

approved

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Last modified November 29 03:18 EST 2022. Contains 358422 sequences. (Running on oeis4.)