A270762
Total sum of the sizes of all blocks with maximal element 8 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
10279, 39848, 174029, 838485, 4395802, 24825947, 149888167, 961547874, 6521484087, 46567171489, 348842020704, 2733150610201, 22336983535651, 189972322541416, 1677852685522313, 15360428047484945, 145515022547392842, 1424312554941600127, 14384441797357797779
Offset: 8
-
b[n_, m_, t_] := b[n, m, t] = If[n == 0, {1, 0}, Sum[If[t == 1 && j != m + 1, 0, Function[p, p + If[j == -t || t == 1 && j == m + 1, {0, p[[1]]}, 0]][b[n - 1, Max[m, j], If[t == 1 && j == m + 1, -j, If[t < 0, t, If[t > 0, t - 1, 0]]]]]], {j, 1, m + 1}]];
a[n_] := b[n, 0, Max[0, 1 + n - 8]][[2]];
Array[a, 24, 8] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)
A270763
Total sum of the sizes of all blocks with maximal element 9 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
54267, 230884, 1090335, 5624233, 31336468, 187018111, 1187718179, 7984210898, 56562256041, 420709044049, 3275003008250, 26608043757997, 225076163325759, 1977999456151260, 18024710156370739, 170022295940977197, 1657528265315075476, 16676976427179730819
Offset: 9
-
b[n_, m_, t_] := b[n, m, t] = If[n == 0, {1, 0}, Sum[If[t == 1 && j != m + 1, 0, Function[p, p + If[j == -t || t == 1 && j == m + 1, {0, p[[1]]}, 0]][b[n - 1, Max[m, j], If[t == 1 && j == m + 1, -j, If[t < 0, t, If[t > 0, t - 1, 0]]]]]], {j, 1, m + 1}]];
a[n_] := b[n, 0, Max[0, 1 + n - 9]][[2]];
Array[a, 24, 9] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)
A270764
Total sum of the sizes of all blocks with maximal element 10 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
306298, 1416047, 7182335, 39465366, 232773295, 1463322425, 9749390152, 68521246341, 506044752411, 3914022281500, 31613966755737, 265988973944593, 2326016924813242, 21099313483973011, 198180280866810827, 1924398094428234590, 19290427455201221715
Offset: 10
-
b[n_, m_, t_] := b[n, m, t] = If[n == 0, {1, 0}, Sum[If[t == 1 && j != m + 1, 0, Function[p, p + If[j == -t || t == 1 && j == m + 1, {0, p[[1]]}, 0]][b[n - 1, Max[m, j], If[t == 1 && j == m + 1, -j, If[t < 0, t, If[t > 0, t - 1, 0]]]]]], {j, 1, m + 1}]];
a[n_] := b[n, 0, Max[0, 1 + n - 10]][[2]];
Array[a, 24, 10] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)
A270765
Total sum of the sizes of all blocks with minimal element 2 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
1, 4, 16, 67, 299, 1429, 7307, 39848, 230884, 1416047, 9160977, 62316137, 444424965, 3314372728, 25786012724, 208842481687, 1757367578867, 15337268316933, 138603393210479, 1295082562497364, 12494759080718152, 124314054484739035, 1274003246005735449
Offset: 2
A270766
Total sum of the sizes of all blocks with minimal element 3 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
2, 9, 41, 195, 979, 5204, 29278, 174029, 1090335, 7182335, 49620133, 358677988, 2706692878, 21279580773, 173959285361, 1476140369523, 12980688801711, 118115459494648, 1110587753256570, 10776530860299409, 107787449481730311, 1110043901404359391
Offset: 3
A270767
Total sum of the sizes of all blocks with minimal element 4 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
5, 25, 127, 670, 3702, 21485, 131007, 838485, 5624233, 39465366, 289162042, 2208190845, 17544083557, 144774580209, 1238893540107, 10977721223490, 100583317230394, 951731543130505, 9288688865151775, 93402218357061709, 966643007728282629, 10286173737875876050
Offset: 4
A270768
Total sum of the sizes of all blocks with minimal element 5 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
15, 82, 456, 2623, 15717, 98367, 643401, 4395802, 31336468, 232773295, 1799100571, 14446912419, 120354176611, 1038736540222, 9275288018740, 85580969753059, 814958928731237, 8000443830761623, 80882083469431805, 841236045441243662, 8992982601018855952
Offset: 5
A270769
Total sum of the sizes of all blocks with minimal element 6 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
52, 307, 1845, 11437, 73561, 492112, 3426532, 24825947, 187018111, 1463322425, 11878759787, 99919924444, 869876263976, 7828394233551, 72744595145117, 697213288063149, 6885160707939613, 69986707107451700, 731580664064312728, 7857203170378852079
Offset: 6
A270770
Total sum of the sizes of all blocks with minimal element 7 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
203, 1283, 8257, 54692, 374718, 2661473, 19610565, 149888167, 1187718179, 9749390152, 82822876970, 727437579645, 6598866824243, 61763271567331, 595865108592205, 5919787896700720, 60506938062384378, 635715591580580381, 6859852419023278269, 75965077760416135623
Offset: 7
A270771
Total sum of the sizes of all blocks with minimal element 8 in all set partitions of {1,2,...,n}.
Original entry on oeis.org
877, 5894, 40338, 283625, 2057641, 15433189, 119762455, 961547874, 7984210898, 68521246341, 607314230475, 5554296859153, 52371126544185, 508651182043282, 5084366849258598, 52260701351731693, 551924896479043065, 5984245105527717453, 66563423916839226915
Offset: 8