A375946
Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^(4/3).
Original entry on oeis.org
1, 4, 32, 372, 5652, 105936, 2360712, 60956472, 1789413864, 58850914752, 2143354213728, 85629122177760, 3723269780412000, 175035687610956480, 8846458578801144000, 478330017277120767360, 27551501517174431852160, 1684176901225092936990720
Offset: 0
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nmax=17; CoefficientList[Series[1 / (1 + 3 * Log[1-x])^(4/3),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)
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a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k+1)*abs(stirling(n, k, 1)));
A375953
Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^(5/2).
Original entry on oeis.org
1, 5, 40, 430, 5770, 92590, 1726940, 36682200, 873793620, 23061929940, 667868085360, 21052931727240, 717531427466280, 26289935772108120, 1030422613932910800, 43018144091244322560, 1905711682795871222160, 89284805444478025826640
Offset: 0
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nmax=17; CoefficientList[Series[1 / (1 + 2 * Log[1 - x])^(5/2),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)
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a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k+2)*abs(stirling(n, k, 1)))/3;
A375987
Expansion of e.g.f. (1 + 2 * log(1 - x))^(3/2).
Original entry on oeis.org
1, -3, 0, 6, 42, 318, 2892, 31944, 424596, 6682740, 122318928, 2559121128, 60275236392, 1577894836248, 45427570253712, 1425885338250432, 48443767097018256, 1770703320887526096, 69273368628184075392, 2887794188011931364576, 127778992241790634125984
Offset: 0
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A375987 := proc(n)
add(mul(2*j-3,j=0..k-1)*abs(stirling1(n,k)),k=0..n) ;
end proc:
seq(A375987(n),n=0..30) ; # R. J. Mathar, Sep 06 2024
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a(n) = sum(k=0, n, prod(j=0, k-1, 2*j-3)*abs(stirling(n, k, 1)));
A375990
Expansion of e.g.f. (1 + 2 * log(1 - x))^2.
Original entry on oeis.org
1, -4, 4, 16, 64, 304, 1712, 11232, 84384, 715392, 6761088, 70513920, 804683520, 9975536640, 133513989120, 1919012014080, 29482606540800, 482183099596800, 8364495012249600, 153406409645260800, 2965940772905779200, 60291976261386240000
Offset: 0
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With[{nn=30},CoefficientList[Series[(1+2Log[1-x])^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 05 2025 *)
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a(n) = if(n==0, 1, -4*(n-1)!+8*abs(stirling(n, 2, 1)));
Showing 1-4 of 4 results.