A377832
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x) ).
Original entry on oeis.org
1, 3, 29, 508, 13137, 452616, 19549021, 1016932512, 61940154177, 4325943203200, 340900244374461, 29927648769380352, 2896829645184711121, 306522175683831195648, 35201889560564096132925, 4360880891670519541927936, 579686447990401730151243009, 82304944815106131595482267648
Offset: 0
A377811
E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^3.
Original entry on oeis.org
1, 4, 27, 283, 4217, 82971, 2041855, 60475885, 2096566449, 83324680435, 3736041351311, 186594364199277, 10274269171279657, 618386703880855339, 40393224245061185919, 2846030947359659421901, 215160957844217080056161, 17373449685399138641312739, 1492298627191467511376377999
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))/(1-x)^3))
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a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2*k+2, n-k)/k!);
A377827
E.g.f. satisfies A(x) = (1 + x)^2 * exp(x * A(x)).
Original entry on oeis.org
1, 3, 13, 106, 1273, 20226, 402589, 9637902, 269967793, 8666441650, 313793596981, 12653878751526, 562489374836041, 27328756018660266, 1440892788988703821, 81940739770677315646, 4999648556871348611425, 325806859913842861709922, 22584652022005415601772645
Offset: 0
A377595
E.g.f. satisfies A(x) = exp( x * A(x) / (1-x) ) / (1-x).
Original entry on oeis.org
1, 2, 11, 103, 1377, 24101, 523813, 13636463, 414246017, 14396807161, 563682761541, 24559156435595, 1178780540094193, 61810491468265541, 3515914378433242997, 215647516162031069191, 14187967957218808201089, 996767406049512569338481, 74478502236949781909301253
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^2))/(1-x)))
-
a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+k, n-k)/k!);
Showing 1-4 of 4 results.