A367789
E.g.f. satisfies A(x) = exp( x/(1-x)^3 * A(x) ).
Original entry on oeis.org
1, 1, 9, 106, 1697, 35076, 893947, 27165706, 960298593, 38751082552, 1758831242291, 88726543365054, 4926355857050641, 298605321687360676, 19623211558172733435, 1389870724939251455506, 105556814502357807727553, 8557797733469700008170224
Offset: 0
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A367789 := proc(n)
n!*add((k+1)^(k-1) * binomial(n+2*k-1,n-k)/k!,k=0..n) ;
end proc:
seq(A367789(n),n=0..70) ; # R. J. Mathar, Dec 04 2023
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))))
A377810
E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^2.
Original entry on oeis.org
1, 3, 17, 154, 1993, 34066, 728209, 18733926, 564117425, 19473863986, 758421401401, 32901791851006, 1573602042306265, 82267318018246986, 4667656830688700801, 285662368622361581206, 18758565855176593500385, 1315663025587514658845026, 98160436697525045768511721
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^2))/(1-x)^2))
-
a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+k+1, n-k)/k!);
A362776
E.g.f. satisfies A(x) = exp( x/(1-x)^2 * A(x)^2 ).
Original entry on oeis.org
1, 1, 9, 127, 2601, 70981, 2433673, 100697787, 4886085137, 272168650441, 17121437245161, 1200717094233559, 92892754255837561, 7859587210132504653, 721996671783802854377, 71564871858940414914451, 7613407794191946986893857, 865285095267929315207801233
Offset: 0
A367790
E.g.f. satisfies A(x) = exp( x/(1-x)^4 * A(x) ).
Original entry on oeis.org
1, 1, 11, 148, 2669, 62056, 1777927, 60692920, 2408692505, 109074596320, 5553702114731, 314208715035304, 19561795753879909, 1329317730339826384, 97924919301787209647, 7773978186375852940696, 661702605336795904770353, 60119367618216155944350400
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 1-5 of 5 results.