A349683
E.g.f. satisfies: log(A(x)) = exp(x*A(x)^3) - 1.
Original entry on oeis.org
1, 1, 8, 131, 3303, 113137, 4909829, 258275887, 15974450676, 1136164798581, 91366516437475, 8197719659916195, 811910298234609913, 87984131560596043801, 10355660409438349522396, 1315550191540192189444535, 179413108433279983993509731
Offset: 0
-
nterms=20;Table[Sum[(3n+1)^(k-1)*StirlingS2[n,k],{k,0,n}],{n,0,nterms-1}] (* Paolo Xausa, Nov 25 2021 *)
-
a(n) = sum(k=0, n, (3*n+1)^(k-1)*stirling(n, k, 2));
A349599
E.g.f. satisfies: log(A(x)) = 1 - exp(-x*A(x)^2).
Original entry on oeis.org
1, 1, 4, 29, 305, 4192, 70875, 1416781, 32551650, 841273527, 24032201213, 747395938962, 24946766300549, 880465276003861, 32274320771151308, 1197240324544640433, 42849289206116498093, 1304855947753532683776, 14954863230501575196551, -2798084168801754024136463
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*(2*n+1)^(k-1)*stirling(n, k, 2));
A362467
E.g.f. satisfies log(A(x)) = exp(x / A(x)^2) - 1.
Original entry on oeis.org
1, 1, -2, 11, -97, 1162, -17401, 309297, -6284804, 141430821, -3411964025, 84469913200, -1971020234987, 31982106694501, 703663251081166, -131978337454653865, 11571772746664732291, -879307513026396837470, 64266964230133042267891
Offset: 0
-
a(n) = sum(k=0, n, (-2*n+1)^(k-1)*stirling(n, k, 2));
A363302
E.g.f. satisfies log(A(x)) = exp(x / A(x)^3) - 1.
Original entry on oeis.org
1, 1, -4, 41, -681, 15667, -460903, 16519141, -698242716, 34004778783, -1874858325725, 115438582354977, -7851013349413919, 584508287058281419, -47281383017104676456, 4129206143361098225405, -387216724567657721607901, 38806186875022459923785751
Offset: 0
-
a(n) = sum(k=0, n, (-3*n+1)^(k-1)*stirling(n, k, 2));
A375868
E.g.f. satisfies A(x) = exp( 2 * (exp(x*A(x)) - 1) ).
Original entry on oeis.org
1, 2, 14, 178, 3342, 83594, 2620998, 98968034, 4375295390, 221781470202, 12684194298998, 808136496137810, 56767509202678094, 4359070656483638762, 363283064756899367462, 32658326649544884611010, 3150270056733608259143422, 324571774149991316277596378
Offset: 0
-
a(n) = 2*sum(k=0, n, (2*n+2)^(k-1)*stirling(n, k, 2));
A375869
E.g.f. satisfies A(x) = exp( 3 * (exp(x*A(x)^(2/3)) - 1) ).
Original entry on oeis.org
1, 3, 24, 327, 6405, 164856, 5276523, 202365351, 9055962270, 463552982301, 26725378964169, 1714193590625478, 121100759112660789, 9344673700445352639, 782093803535217656256, 70570503124491323693523, 6829746633650550406177713, 705729134240394228512985960
Offset: 0
-
a(n) = 3*sum(k=0, n, (2*n+3)^(k-1)*stirling(n, k, 2));
Showing 1-6 of 6 results.
Comments