A363355
E.g.f. satisfies A(x) = exp(x * A(x) * (1 + x * A(x)^2)).
Original entry on oeis.org
1, 1, 5, 46, 641, 11996, 282907, 8060242, 269429729, 10341367480, 448317429011, 21667926214694, 1155321200076529, 67370686916807236, 4265392644606677963, 291391173322695366106, 21365209437807863776193, 1673543873372595900318704
Offset: 0
A365013
E.g.f. satisfies A(x) = exp( x*A(x)/(1 - x * A(x)^3) ).
Original entry on oeis.org
1, 1, 5, 58, 1061, 26536, 843457, 32553424, 1478813513, 77304347776, 4571222616701, 301696674682624, 21985118975444077, 1753288356936334336, 151887264799071753785, 14203597499192539334656, 1426051485043745729079953, 153000280727938469281693696
Offset: 0
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Array[#!*Sum[ (3 # - 2 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-2*k+1)^(k-1)*binomial(n-1, n-k)/k!);
A365016
E.g.f. satisfies A(x) = exp( x*A(x)^3/(1 - x * A(x)^2) ).
Original entry on oeis.org
1, 1, 9, 160, 4345, 159796, 7434199, 418864426, 27732988609, 2110729489048, 181587635465671, 17426825999144926, 1845855944285411425, 213900244312057975348, 26919356609721984494311, 3656322063766897691641666, 533110345129065969043548289
Offset: 0
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Array[#!*Sum[ (2 # + k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 17, 0] (* Michael De Vlieger, Aug 18 2023 *)
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a(n) = n!*sum(k=0, n, (2*n+k+1)^(k-1)*binomial(n-1, n-k)/k!);
A372179
E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) / (1 - x * A(x)) ).
Original entry on oeis.org
1, 2, 12, 134, 2232, 49762, 1394236, 47117982, 1866217296, 84810000194, 4350808646964, 248736339576958, 15682868019616408, 1081153176108929250, 80906410246285190508, 6531880775140905838238, 565912845564569155284384, 52373575389612727174282882
Offset: 0
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a(n, r=2, s=1, t=1, u=2) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);
A372183
E.g.f. A(x) satisfies A(x) = exp( x * A(x)^5 / (1 - x * A(x)^2) ).
Original entry on oeis.org
1, 1, 13, 340, 13713, 752516, 52372051, 4421017602, 438996446545, 50142716621848, 6477138263806011, 933667525669154486, 148582199464010331289, 25874197258988478298068, 4894174597530612144797299, 999256176035969437218129946, 219035687330062179838536993441
Offset: 0
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a(n, r=1, s=1, t=5, u=2) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);
Showing 1-5 of 5 results.