A365035
E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).
Original entry on oeis.org
1, 1, 3, 1, -11, 61, 301, -6299, 7561, 903673, -9019079, -145636919, 4305630781, 7516191541, -2037845181371, 22442805921901, 944219385367441, -29922880660473359, -288352494154313999, 32071808922904896913, -273044292430852251899
Offset: 0
A365036
E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^2)).
Original entry on oeis.org
1, 1, 3, -5, -23, 521, -1829, -71021, 1319697, 5905297, -683965709, 8664974891, 311864420473, -13981842414695, 6694007756619, 16448800124183491, -448649039951220959, -13236887251789967071, 1210629233913421852387, -12065049302884271631269
Offset: 0
A365037
E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^3)).
Original entry on oeis.org
1, 1, 3, -11, -11, 1341, -14339, -168923, 8905065, -85313735, -4604578919, 197455645641, -273728455571, -267002430142187, 9427821270512373, 178475402982086701, -28273343910563670959, 713736314833387866225, 51907546734507018043057
Offset: 0
A228563
E.g.f: A(x) = Sum_{n>=0} (1 + x*A(x)^n)^n * x^n/n!.
Original entry on oeis.org
1, 1, 3, 13, 109, 1241, 18541, 340495, 7475721, 191215729, 5590994041, 184086712151, 6745657327069, 272484296020249, 12037353264295269, 577681783128081871, 29946086856245571601, 1668620115204908947937, 99516760157428436346481, 6329149392153729480812839
Offset: 0
-
{a(n)=local(A=1+x);for(i=1,n,A=sum(k=0,n,(1+x*A^k +x*O(x^n))^k*x^k/k!));n!*polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
A372182
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, 334, 13329, 724316, 49939411, 4177202562, 411049275265, 46530896718520, 5957142774561531, 851104158600401366, 134246582420467536289, 23171656877102178017028, 4344395473350526080895843, 879206880413471231912831626, 191028062860784640128743389441
Offset: 0
-
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(s*k, n-k)/k!);