A260578
Coefficients in asymptotic expansion of sequence A259869.
Original entry on oeis.org
1, 0, -2, -6, -29, -196, -1665, -16796, -194905, -2549468, -37055681, -592013436, -10307671769, -194225544124, -3937581243201, -85460277981116, -1977127315636969, -48573021658496348, -1262954975286604673, -34650561545808167292, -1000438355724912080873
Offset: 0
A259869(n) / (n!/exp(1)) ~ 1 - 2/n^2 - 6/n^3 - 29/n^4 - 196/n^5 - 1665/n^6 - ...
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nmax = 20; b = CoefficientList[Assuming[Element[x, Reals], Series[x^2*E^(2 + 2/x)/ExpIntegralEi[1 + 1/x]^2, {x, 0, nmax}]], x]; Flatten[{1, Table[Sum[b[[k+1]]*StirlingS2[n-1, k-1], {k, 1, n}], {n, 1, nmax}]}] (* Vaclav Kotesovec, Aug 03 2015 *)
A259870
a(0)=0, a(1)=1; a(n) = n*a(n-1) + (n-2)*a(n-2) - Sum_{j=1..n-1} a(j)*a(n-j).
Original entry on oeis.org
0, 1, 1, 2, 5, 17, 74, 401, 2609, 19802, 171437, 1664585, 17892938, 210771761, 2698597601, 37301188610, 553473138677, 8773014886289, 147928235322314, 2643635547262049, 49909639472912177, 992516629078846010, 20736210820909594109, 454084963076923193321
Offset: 0
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nmax = 25; CoefficientList[Assuming[Element[x, Reals], Series[-1/(ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] - 1) - 1, {x, 0, nmax}]], x] (* Vaclav Kotesovec, Aug 05 2015 *)
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a=vector(30); a[1]=0; a[2]=1; for(n=2, #a-1, a[n+1] = n*a[n] + (n-2)*a[n-1] - sum(j=1, n-1, a[j+1]*a[n-j+1])); a \\ Colin Barker, Jul 09 2015
A260949
Coefficients in asymptotic expansion of sequence A259871.
Original entry on oeis.org
1, 4, 16, 76, 416, 2576, 17840, 137268, 1170104, 11050940, 115885968, 1353366864, 17640817784, 256630492660, 4153220868128, 74315436120300, 1458541231513152, 31131651836906752, 716862465409883040, 17683184383300077828, 464519709712796199816
Offset: 0
A259871(n)/((n-1)!/exp(1)) ~ 1 + 4/n + 16/n^2 + 76/n^3 + 416/n^4 + 2576/n^5 + ...
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nmax = 25; b = CoefficientList[Assuming[Element[x, Reals], Series[x/(2*ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] - 1)^2, {x, 0, nmax+1}]], x]; Table[Sum[b[[k+1]]*StirlingS2[n, k-1], {k, 1, n+1}], {n, 0, nmax}]
A260950
Coefficients in asymptotic expansion of sequence A259872.
Original entry on oeis.org
1, -2, 1, 1, -10, -61, -382, -3489, -39001, -484075, -6619449, -99610098, -1638687448, -29255834780, -563343011377, -11639759292186, -256916737692132, -6034068201092777, -150271333127027481, -3955735249215111270, -109757859467421502791
Offset: 0
A259872(n)/((n-1)!/exp(1)) ~ 1 - 2/n + 1/n^2 + 1/n^3 - 10/n^4 - 61/n^5 - ...
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nmax = 25; b = CoefficientList[Assuming[Element[x, Reals], Series[x/(ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] + 1)^2, {x, 0, nmax+1}]], x]; Table[Sum[b[[k+1]]*StirlingS2[n, k-1], {k, 1, n+1}], {n, 0, nmax}]
A305275
Coefficients in asymptotic expansion of sequence A302557.
Original entry on oeis.org
1, 0, 2, 6, 35, 256, 2187, 21620, 243947, 3098528, 43799819, 682540780, 11630529643, 215190967544, 4296657514283, 92083313483300, 2108244638675035, 51350077108834832, 1325682930813985547, 36157047428501464220, 1038793351537388253211, 31354977545074731373512
Offset: 0
A302557(n) / (exp(-1) * n!) ~ 1 + 2/n^2 + 6/n^3 + 35/n^4 + 256/n^5 + 2187/n^6 + ...
Showing 1-5 of 5 results.
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