A361143
E.g.f. satisfies A(x) = exp( x*A(x)^4/(1 - x*A(x)^2) ).
Original entry on oeis.org
1, 1, 11, 241, 8105, 370061, 21403675, 1500521485, 123685912817, 11724012791929, 1256517775425131, 150254377493878505, 19833528195709809817, 2864566162751107839493, 449364739762263286489403, 76084967168410028438252101, 13829896583435315152843525985
Offset: 0
A363357
E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x))).
Original entry on oeis.org
1, 1, 7, 85, 1581, 39501, 1244953, 47426373, 2120506489, 108894505753, 6317267871501, 408637512353049, 29164082035045477, 2276557391070945477, 192956160476285907457, 17647873882378895267821, 1732445579330211460781937, 181694902682241512454842673
Offset: 0
A364942
E.g.f. satisfies A(x) = exp( x*A(x)^2 / (1 - x*A(x))^3 ).
Original entry on oeis.org
1, 1, 11, 193, 5037, 176221, 7755433, 411995529, 25665442841, 1835264297881, 148192928581581, 13338664928207389, 1324344628799752981, 143792046846092303829, 16949599953405295395521, 2155710634160924802161041, 294250014166281073851809457
Offset: 0
A364941
E.g.f. satisfies A(x) = exp( x*A(x)^2 / (1 - x*A(x))^2 ).
Original entry on oeis.org
1, 1, 9, 139, 3201, 98861, 3842653, 180342471, 9926870145, 627296384665, 44766115252821, 3561306199330859, 312531347680052449, 29994317717748851013, 3125271184480991706189, 351360521075659460743471, 42395667639523579933634817, 5464885215245368415146646321
Offset: 0
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Join[{1}, Table[n! * Sum[(n+k+1)^(k-1) * Binomial[n+k-1,n-k]/k!, {k,0,n}], {n,1,20}]] (* Vaclav Kotesovec, Nov 18 2023 *)
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a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(n+k-1, n-k)/k!);
A365014
E.g.f. satisfies A(x) = exp( x*A(x)^2/(1 - x * A(x)^3) ).
Original entry on oeis.org
1, 1, 7, 103, 2349, 72961, 2874793, 137399487, 7724650601, 499542475105, 36532938744621, 2981405776356679, 268605245211618637, 26480489709604968129, 2835590837094928349921, 327748240537910056251151, 40669893396736296241364817, 5392699633877586027282801217
Offset: 0
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Array[#!*Sum[ (3 # - k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)
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a(n) = n!*sum(k=0, n, (3*n-k+1)^(k-1)*binomial(n-1, n-k)/k!);
Showing 1-5 of 5 results.