A361093
E.g.f. satisfies A(x) = exp( 1/(1 - x * A(x)^2) - 1 ).
Original entry on oeis.org
1, 1, 7, 97, 2049, 58541, 2114143, 92419965, 4746108769, 280105517881, 18683156508471, 1389960074426969, 114119472522112225, 10249863809271551973, 999746622121255094479, 105236583967331849218741, 11891012005206169120252737, 1435560112909007680593616625
Offset: 0
-
Table[n! * Sum[(2*n+1)^(k-1) * Binomial[n-1,n-k]/k!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Mar 02 2023 *)
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a(n) = n!*sum(k=0, n, (2*n+1)^(k-1)*binomial(n-1, n-k)/k!);
A361094
E.g.f. satisfies A(x) = exp( 1/(1 - x * A(x)^3) - 1 ).
Original entry on oeis.org
1, 1, 9, 166, 4717, 182136, 8911549, 528571408, 36864033945, 2956595372416, 268116203622961, 27128338649300736, 3029974270053623941, 370289278173654092800, 49150116757136815109733, 7041536364582774222616576, 1083004122024520209576760369
Offset: 0
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Table[n! * Sum[(3*n+1)^(k-1) * Binomial[n-1,n-k]/k!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Mar 02 2023 *)
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a(n) = n!*sum(k=0, n, (3*n+1)^(k-1)*binomial(n-1, n-k)/k!);
A361095
E.g.f. satisfies A(x) = exp( 1/(1 - x/A(x)) - 1 ).
Original entry on oeis.org
1, 1, 1, -2, -3, 56, -155, -2736, 34489, 72064, -6599799, 53676800, 1155350581, -32238425088, -3604716947, 14790925735936, -235482791871375, -4972572910452736, 254158358486634001, -1028499606209101824, -202204782754527137939, 5371925138905661440000
Offset: 0
-
a(n) = if(n==0, 1, n!*sum(k=1, n, (-n+1)^(k-1)*binomial(n-1, n-k)/k!));
A361096
E.g.f. satisfies A(x) = exp( 1/(1 - x/A(x)^2) - 1 ).
Original entry on oeis.org
1, 1, -1, 1, 17, -339, 4999, -63587, 566145, 3549241, -405637489, 15518099961, -446235202799, 9617693853925, -75522664207017, -7341781870733099, 596513949276803969, -30104875035438797583, 1144712508931072057375, -27381639204739332379151
Offset: 0
A361092
E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)^3) ).
Original entry on oeis.org
1, 1, 3, -5, -107, 1041, 20701, -440033, -8464455, 343190593, 5639857561, -423764450889, -4968055259771, 754544622295153, 3846355902999429, -1818148417882379729, 6637679490204153841, 5658469355898945338625, -84578525845602646639823
Offset: 0
Showing 1-5 of 5 results.