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 *)
A259871
a(0)=1/2, a(1)=1; a(n) = n*a(n-1) + (n-2)*a(n-2) - 2*Sum_{j=1..n-1} a(j)*a(n-j) + 2*Sum_{j=0..n-1} a(j)*a(n-1-j).
Original entry on oeis.org
1, 2, 5, 14, 45, 170, 777, 4350, 29513, 236530, 2179133, 22576206, 258821269, 3245286490, 44115311969, 645664173566, 10117122765905, 168922438409826, 2993228077070645, 56090022818326542, 1108099905463382973, 23015655499699484810, 501356717394207256441
Offset: 1
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nmax = 25; Rest[CoefficientList[Assuming[Element[x, Reals], Series[-1/(2*ExpIntegralEi[1 + 1/x]/Exp[1 + 1/x] - 1)/2, {x, 0, nmax}]], x]] (* Vaclav Kotesovec, Aug 05 2015 *)
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@CachedFunction
def a(n) : return 1 if n==1 else 2 if n==2 else (n+2)*a(n-1) + (n-2)*a(n-2) - 2*sum(a(j)*a(n-j) for j in [1..n-1]) + 2*sum(a(j)*a(n-1-j) for j in [1..n-2])
A260948
Coefficients in asymptotic expansion of sequence A259870.
Original entry on oeis.org
1, 2, 5, 17, 74, 395, 2526, 19087, 168603, 1723065, 20148031, 266437102, 3938754720, 64391209604, 1152961464743, 22424127879610, 470399253269776, 10579865622308851, 253840801521314095, 6468953273455413674, 174452533187403980841, 4962228907578051232358
Offset: 0
A259870(n)/((n-1)!/exp(1)) ~ 1 + 2/n + 5/n^2 + 17/n^3 + 74/n^4 + 395/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}]
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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