A365283
E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^2*A(x)^2).
Original entry on oeis.org
1, 1, 2, 12, 120, 1380, 19440, 341040, 7029120, 164762640, 4355769600, 128527439040, 4181332700160, 148633442717760, 5734427199621120, 238676208285715200, 10659325532663808000, 508452777299622355200, 25800664274991135129600
Offset: 0
-
Join[{1},Table[n!/(n+1) * Sum[(n-2*k)^k * Binomial[n+1,n-2*k]/k!, {k, 0, Floor[n/2]}], {n,1,20}]] (* Vaclav Kotesovec, Nov 08 2023 *)
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a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(n+1, n-2*k)/k!)/(n+1);
A365285
E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^3*A(x)).
Original entry on oeis.org
1, 1, 2, 6, 48, 480, 5040, 57960, 806400, 13426560, 250992000, 5102697600, 113283878400, 2760905347200, 73287883468800, 2093750122464000, 63947194517606400, 2082970788291993600, 72182922107859763200, 2651026034089585152000
Offset: 0
A365284
E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^2*A(x)^3).
Original entry on oeis.org
1, 1, 2, 12, 144, 1980, 31680, 630840, 15093120, 411883920, 12607660800, 430740858240, 16265744732160, 671629503504960, 30093198326231040, 1454898560062147200, 75503612563771392000, 4186035286381024876800, 246916968958719605145600
Offset: 0
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Join[{1}, Table[n! * Sum[(n - 2*k)^k*Binomial[n + k + 1, n - 2*k]/((n + k + 1)*k!), {k, 0, Floor[n/2]}], {n, 1, 20}]] (* Vaclav Kotesovec, Mar 10 2024 *)
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a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(n+k+1, n-2*k)/((n+k+1)*k!));
A371043
E.g.f. satisfies A(x) = 1 + x^2*A(x)*exp(x*A(x)).
Original entry on oeis.org
1, 0, 2, 6, 36, 380, 3630, 47082, 725816, 12132360, 235801530, 5083309550, 119757623172, 3103443520476, 87082536196838, 2632399338834930, 85471932351187440, 2961803643600574352, 109154615479427298546, 4264407640037365789014, 175984871341042826680700
Offset: 0
Showing 1-4 of 4 results.