A367080
E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2).
Original entry on oeis.org
1, 1, 5, 50, 766, 15914, 418548, 13337624, 499600848, 21516318360, 1047593782440, 56903921842272, 3411723783002016, 223803339516120480, 15944855840879771232, 1226078375934824887680, 101209861891840507123200, 8926972851724904613537792
Offset: 0
-
Table[(2*n)! * Sum[Abs[StirlingS1[n,k]]/(2*n-k+1)!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)
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a(n) = (2*n)!*sum(k=0, n, abs(stirling(n, k, 1))/(2*n-k+1)!);
A377323
E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3)/A(x).
Original entry on oeis.org
1, 1, 5, 53, 884, 20234, 589834, 20903700, 872660256, 41944510752, 2281437791448, 138539360885760, 9290720296262976, 681965664411820944, 54384461861952738528, 4682101594725064872768, 432815761314471190599936, 42757813607285233998385920, 4495579313771176952867958528
Offset: 0
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a(n) = sum(k=0, n, (3*n-k)!/(3*n-2*k+1)!*abs(stirling(n, k, 1)));
A367079
E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 5, 47, 654, 12084, 278682, 7708056, 248678784, 9168447600, 380274659760, 17524760349216, 888364833282000, 49125202031205936, 2942774373267939168, 189829708902667840320, 13118899353628035596544, 966975804677206274688000
Offset: 0
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Table[(3*n)! * Sum[StirlingS1[n,k]/(3*n-k+1)!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)
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a(n) = (3*n)!*sum(k=0, n, stirling(n, k, 1)/(3*n-k+1)!);
A377327
E.g.f. satisfies A(x) = 1 - A(x)^2 * log(1 - x*A(x)^3).
Original entry on oeis.org
1, 1, 11, 251, 8858, 425534, 25928068, 1916213928, 166580610504, 16657218047328, 1883646389742624, 237695994684785592, 33113333472295201536, 5047818696187818951984, 835818979837614364874496, 149383091745519898076484480, 28663410267058615074689247360, 5877004345535507714104006175616
Offset: 0
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a(n) = sum(k=0, n, (3*n+2*k)!/(3*n+k+1)!*abs(stirling(n, k, 1)));
A377350
E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3)/A(x)^3.
Original entry on oeis.org
1, 1, 1, 11, 108, 1584, 29808, 674988, 18091944, 557844408, 19468760904, 758698622472, 32653135227936, 1538316755200224, 78737559447563136, 4350956519444451840, 258163046132873143680, 16370486288763937324416, 1104824513292622360789248, 79068747951669626322531840
Offset: 0
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a(n) = sum(k=0, (3*n+1)\4, (3*n-3*k)!/(3*n-4*k+1)!*abs(stirling(n, k, 1)));
A377361
E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x)) )^3.
Original entry on oeis.org
1, 3, 27, 435, 10308, 324942, 12831540, 610024398, 33948639024, 2165995595208, 155913776865216, 12501945620113320, 1105228405532295216, 106806396107364409440, 11201958792185117156640, 1267313834232739887340464, 153842580381390055963315200, 19946923686925035463312117632
Offset: 0
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a(n) = 3*(3*n+2)!*sum(k=0, n, abs(stirling(n, k, 1))/(3*n-k+3)!);
Showing 1-6 of 6 results.
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