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A332942 Number of entries in the second blocks of all set partitions of [n] when blocks are ordered by increasing lengths. 2
1, 7, 25, 101, 366, 1555, 7099, 34627, 184033, 1059972, 6425992, 41266681, 280938451, 2009636335, 15025372685, 117386912433, 956458929950, 8104399834719, 71244441818927, 648761935841876, 6110827367541999, 59454153443971106, 596654820386392152 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..576

Wikipedia, Partition of a set

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,

      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,

      max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))

    end:

a:= n-> b(n, 1, 2)[2]:

seq(a(n), n=2..24);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, t_] := b[n, i, t] = If[n == 0, {1, 0}, If[i > n, 0 {0, 0}, Sum[ Function[p, p + If[t > 0 && t - j < 1, {0, p[[1]]*i}, {0, 0}]][b[n - i*j, i + 1, Max[0, t - j]]/j!*multinomial[n, Append[Table[i, {j}], n - i*j]]], {j, 0, n/i}]]];

a[n_] := b[n, 1, 2][[2]];

a /@ Range[2, 24] (* Jean-Fran├žois Alcover, Jan 06 2021, after Alois P. Heinz *)

CROSSREFS

Column k=2 of A319298.

Sequence in context: A304421 A138729 A035509 * A247173 A141627 A289606

Adjacent sequences:  A332939 A332940 A332941 * A332943 A332944 A332945

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2020

STATUS

approved

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Last modified October 3 14:02 EDT 2022. Contains 357237 sequences. (Running on oeis4.)