A087138
Expansion of (1-sqrt(1-4*log(1+x)))/2.
Original entry on oeis.org
1, 1, 8, 64, 824, 12968, 252720, 5789712, 153169440, 4589004192, 153643615872, 5684390364288, 230307823878144, 10141452865049088, 482259966649655808, 24630247225278881280, 1344614199041549399040, 78137673004382654223360
Offset: 1
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Rest[CoefficientList[Series[(1-Sqrt[1-4*Log[1+x]])/2, {x, 0, 20}], x] * Range[0, 20]!] (* Vaclav Kotesovec, May 03 2015 *)
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x='x+O('x^50); Vec(serlaplace((1-sqrt(1-4*log(1+x)))/2)) \\ G. C. Greubel, May 24 2017
A370463
E.g.f. satisfies A(x) = log(1 + x)/(1 - A(x))^3.
Original entry on oeis.org
0, 1, 5, 74, 1704, 54474, 2225394, 110786976, 6506273544, 440368208280, 33752787590136, 2889747086330400, 273333159994125984, 28307010099549881088, 3185660442523728449664, 387117483236717961052800, 50518567433159392237036416, 7046383438320021239186859264
Offset: 0
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a(n) = sum(k=1, n, (4*k-2)!/(3*k-1)!*stirling(n, k, 1));
A371314
E.g.f. satisfies A(x) = -log(1 - x)/(1 - A(x))^2.
Original entry on oeis.org
0, 1, 5, 56, 1022, 26054, 853426, 34150584, 1614418536, 88035438144, 5439554576064, 375580703703072, 28658577826251072, 2394815612176027104, 217504341217879448352, 21333409628052488832768, 2247318076016738768083200, 253054488675536428638723840
Offset: 0
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A371314 := proc(n)
add((3*k-2)!/(2*k-1)!*abs(stirling1(n,k)),k=1..n) ;
end proc:
seq(A371314(n),n=0..40) ; # R. J. Mathar, Mar 25 2024
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Table[Sum[(3*k-2)!/(2*k-1)! * Abs[StirlingS1[n, k]], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 19 2024 *)
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a(n) = sum(k=1, n, (3*k-2)!/(2*k-1)!*abs(stirling(n, k, 1)));
A371326
E.g.f. satisfies A(x) = log(1 + x/(1 - A(x)))/(1 - A(x))^2.
Original entry on oeis.org
0, 1, 5, 71, 1606, 50334, 2017840, 98597204, 5684225640, 377709287232, 28423701233784, 2389343434217376, 221907620769333648, 22565504728129558272, 2493614778861026071584, 297548320679718887153088, 38128996565367754662297600, 5222327925855459163424791680
Offset: 0
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a(n) = sum(k=1, n, (n+3*k-2)!/(n+2*k-1)!*stirling(n, k, 1));
Showing 1-4 of 4 results.