The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A327631 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A327631

Number T(n,k) of parts in all proper k-times partitions of n; triangle T(n,k), n >= 1, 0 <= k <= n-1, read by rows.
(history; published version)

#39 by Susanna Cuyler at Tue Jan 07 09:10:58 EST 2020

STATUS

proposed

approved

#38 by Jean-François Alcover at Tue Jan 07 05:15:03 EST 2020

STATUS

editing

proposed

#37 by Jean-François Alcover at Tue Jan 07 05:14:59 EST 2020

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[k == 0, {1, 1}, If[i < 2, 0, b[n, i - 1, k]] + Function[h, Function[f, f + {0, f[[1]]*h[[2]]/ h[[1]]}][h[[1]]*b[n - i, Min[n - i, i], k]]][b[i, i, k - 1]]]];

T[n_, k_] := Sum[b[n, n, i][[2]]*(-1)^(k - i)*Binomial[k, i], {i, 0, k}];

Table[T[n, k], {n, 1, 12}, {k, 0, n - 1}] // Flatten (* Jean-François Alcover, Jan 07 2020, after Alois P. Heinz *)

STATUS

approved

editing

#36 by Alois P. Heinz at Wed Oct 02 20:04:09 EDT 2019

STATUS

editing

approved

#35 by Alois P. Heinz at Wed Oct 02 18:18:23 EDT 2019

CROSSREFS

Columns k=0-1 2 give: A057427, -1+A006128(n), A328042.

#34 by Alois P. Heinz at Wed Oct 02 18:14:43 EDT 2019

CROSSREFS

T(n,floor(n/2)) gives A328041.

STATUS

approved

editing

#33 by Alois P. Heinz at Sun Sep 29 13:18:19 EDT 2019

STATUS

editing

approved

#32 by Alois P. Heinz at Sun Sep 29 13:17:44 EDT 2019

CROSSREFS

Column Columns k=0 gives -1 give: A057427, -1+A006128(n).

STATUS

approved

editing

#31 by Alois P. Heinz at Fri Sep 20 22:18:58 EDT 2019

STATUS

editing

approved

#30 by Alois P. Heinz at Fri Sep 20 19:23:17 EDT 2019

CROSSREFS

Row sums give A327648.

STATUS

approved

editing