A270497
Sum of the sizes of the fifth blocks in all set partitions of {1,2,...,n}.
Original entry on oeis.org
1, 17, 184, 1641, 13276, 102244, 770989, 5795889, 43967302, 339403001, 2681449074, 21763977864, 181900742989, 1567473197429, 13932812925824, 127738400615689, 1207445992487256, 11759938209394472, 117926100082535985, 1216563820893322317, 12901060857158377838
Offset: 5
-
b:= proc(n, m) option remember; `if`(n=0, [1, 0],
add((p->`if`(j<6, [p[1], p[2]+p[1]*x^j], p))(
b(n-1, max(m, j))), j=1..m+1))
end:
a:= n-> coeff(b(n, 0)[2], x, 5):
seq(a(n), n=5..30);
-
b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 6, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := Coefficient[b[n, 0][[2]], x, 5];
Table[a[n], {n, 5, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)
A270498
Sum of the sizes of the sixth blocks in all set partitions of {1,2,...,n}.
Original entry on oeis.org
1, 23, 324, 3645, 36223, 334751, 2965654, 25691104, 220643295, 1897548384, 16463907354, 144927422746, 1299763249771, 11912250951457, 111803042249042, 1076045623549383, 10628068291940557, 107760039986995689, 1121581530251066296, 11980190581723881858
Offset: 6
-
b:= proc(n, m) option remember; `if`(n=0, [1, 0],
add((p->`if`(j<7, [p[1], p[2]+p[1]*x^j], p))(
b(n-1, max(m, j))), j=1..m+1))
end:
a:= n-> coeff(b(n, 0)[2], x, 6):
seq(a(n), n=6..30);
-
b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 7, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := Coefficient[b[n, 0][[2]], x, 6];
Table[a[n], {n, 6, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)
A270499
Sum of the sizes of the seventh blocks in all set partitions of {1,2,...,n}.
Original entry on oeis.org
1, 30, 536, 7473, 90223, 995191, 10354804, 103779309, 1016654053, 9840330258, 94884791378, 917358452410, 8938608738199, 88139900141632, 882388425916186, 8991438542446875, 93434278760386701, 991477889069432577, 10753621593467498170, 119276548511953973463
Offset: 7
-
b:= proc(n, m) option remember; `if`(n=0, [1, 0],
add((p->`if`(j<8, [p[1], p[2]+p[1]*x^j], p))(
b(n-1, max(m, j))), j=1..m+1))
end:
a:= n-> coeff(b(n, 0)[2], x, 7):
seq(a(n), n=7..30);
-
b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 8, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := Coefficient[b[n, 0][[2]], x, 7];
Table[a[n], {n, 7, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)
A270500
Sum of the sizes of the eighth blocks in all set partitions of {1,2,...,n}.
Original entry on oeis.org
1, 38, 842, 14303, 207186, 2704647, 32890525, 380797185, 4261887992, 46630717274, 503083676180, 5388429971042, 57614949228381, 617784630625192, 6668316674283818, 72685580775510461, 802184346241503206, 8983104653288906449, 102246823195952449865
Offset: 8
-
b:= proc(n, m) option remember; `if`(n=0, [1, 0],
add((p->`if`(j<9, [p[1], p[2]+p[1]*x^j], p))(
b(n-1, max(m, j))), j=1..m+1))
end:
a:= n-> coeff(b(n, 0)[2], x, 8):
seq(a(n), n=8..30);
-
b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 9, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := Coefficient[b[n, 0][[2]], x, 8];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)
A270501
Sum of the sizes of the ninth blocks in all set partitions of {1,2,...,n}.
Original entry on oeis.org
1, 47, 1267, 25820, 443249, 6782968, 95737722, 1274661371, 16262852622, 201150251360, 2433394489974, 28994047438464, 342194356303003, 4019284858043011, 47169786677194389, 555004306379162344, 6566292430043177959, 78313245092235242824, 943595956075419339524
Offset: 9
-
b:= proc(n, m) option remember; `if`(n=0, [1, 0],
add((p->`if`(j<10, [p[1], p[2]+p[1]*x^j], p))(
b(n-1, max(m, j))), j=1..m+1))
end:
a:= n-> coeff(b(n, 0)[2], x, 9):
seq(a(n), n=9..30);
-
b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 10, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := Coefficient[b[n, 0][[2]], x, 9];
Table[a[n], {n, 9, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)
A270502
Sum of the sizes of the tenth blocks in all set partitions of {1,2,...,n}.
Original entry on oeis.org
1, 57, 1839, 44346, 891892, 15848311, 257647088, 3921554995, 56796169899, 792102157717, 10734723141617, 142380931674179, 1858965371935248, 24006134113802346, 307860388231938976, 3934302726222970593, 50254089923100713719, 643301179860716506788
Offset: 10
-
b:= proc(n, m) option remember; `if`(n=0, [1, 0],
add((p->`if`(j<11, [p[1], p[2]+p[1]*x^j], p))(
b(n-1, max(m, j))), j=1..m+1))
end:
a:= n-> coeff(b(n, 0)[2], x, 10):
seq(a(n), n=10..30);
-
b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 11, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := Coefficient[b[n, 0][[2]], x, 10];
Table[a[n], {n, 10, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)