A371230
E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 128, 750, 29964, 377160, 15795072, 329631120, 15001287120, 449174341440, 22551082739712, 885381886509120, 49302509206648320, 2391802812599316480, 147728974730632012800, 8502972330919072688640, 580806950108814502345728
Offset: 0
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terms=19; A[]=1; Do[A[x]= 1 - x*A[x]^3*Log[1 - x*A[x]^2] + O[x]^terms//Normal, terms]; CoefficientList[Series[A[x],{x,0,terms}],x]*Range[0,terms-1]! (* Stefano Spezia, Sep 03 2025 *)
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a(n) = n!*sum(k=0, n\2, (2*n+k)!*abs(stirling(n-k, k, 1))/(n-k)!)/(2*n+1)!;
A371229
E.g.f. satisfies A(x) = 1 - x*A(x)^2*log(1 - x*A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 104, 630, 19944, 259560, 8718464, 185086944, 6914815200, 206059083120, 8700740615808, 332779651158240, 15916427365716864, 738672634596405600, 39847940942657495040, 2163098542598925281280, 130682368989193123952640
Offset: 0
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a(n) = n!*(2*n)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(2*n-k+1)!));
A371262
E.g.f. satisfies A(x) = 1 + x * (exp(x*A(x)^2) - 1).
Original entry on oeis.org
1, 0, 2, 3, 52, 365, 5286, 76867, 1341320, 27823833, 624467530, 16163482511, 452003629452, 13975370745349, 467133121195118, 16865722845267675, 653859200911607056, 27061461284541490097, 1192488605596282310802, 55686113074253206544167
Offset: 0
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a(n) = n!*sum(k=0, n\2, (2*n-2*k)!*stirling(n-k, k, 2)/((n-k)!*(2*n-3*k+1)!));
A371228
E.g.f. satisfies A(x) = 1 - x*A(x)*log(1 - x*A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 80, 510, 12084, 164640, 4272736, 91935648, 2769703920, 80692896240, 2849745645504, 103479044628960, 4250475820200960, 183436357950387360, 8649275730513361920, 430735131434242736640, 22999938416454315239424, 1295673669960473064844800
Offset: 0
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a(n) = n!*sum(k=0, n\2, (2*n-k)!*abs(stirling(n-k, k, 1))/((n-k)!*(2*n-2*k+1)!));
A377685
E.g.f. satisfies A(x) = (1 - x * log(1 - x*A(x)))^2.
Original entry on oeis.org
1, 0, 4, 6, 136, 900, 16308, 229320, 4691104, 99156960, 2481162480, 67862678400, 2063842827264, 68473763804160, 2468786906210688, 96048626176339200, 4010912604492410880, 178968539487145282560, 8496991445958129576960, 427734144995749047152640
Offset: 0
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a(n) = 2*n!*sum(k=0, n\2, (2*n-2*k+1)!*abs(stirling(n-k, k, 1))/((n-k)!*(2*n-3*k+2)!));
A377687
E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)^3).
Original entry on oeis.org
1, 0, 2, 3, 80, 570, 12744, 198660, 4969152, 119968128, 3607836480, 115031711520, 4163170478400, 162622297300320, 6952158785424384, 319741032356928000, 15818989359665802240, 835755271882288128000, 47015148988105365288960, 2804276310235518168161280
Offset: 0
-
a(n) = n!*sum(k=0, n\2, (3*n-3*k)!*abs(stirling(n-k, k, 1))/((n-k)!*(3*n-4*k+1)!));
Showing 1-6 of 6 results.