A367835
Expansion of e.g.f. 1/(2 - x - exp(2*x)).
Original entry on oeis.org
1, 3, 22, 242, 3544, 64872, 1424976, 36517840, 1069533824, 35240047232, 1290137297152, 51955085596416, 2282489348834304, 108630445541684224, 5567741266098944000, 305752314499878569984, 17909736027185859100672, 1114647522476340562132992
Offset: 0
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A367835 := proc(n)
option remember ;
if n = 0 then
1 ;
else
n*procname(n-1)+add(2^k*binomial(n,k)*procname(n-k),k=1..n) ;
end if;
end proc:
seq(A367835(n),n=0..70) ; # R. J. Mathar, Dec 04 2023
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;
A367836
Expansion of e.g.f. 1/(2 - x - exp(3*x)).
Original entry on oeis.org
1, 4, 41, 627, 12759, 324543, 9906453, 352785933, 14358074211, 657405969075, 33444798498657, 1871613674744553, 114259520317835871, 7556674046930376111, 538212358684663414317, 41071433946325564954581, 3343141735414440335583003
Offset: 0
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With[{nn=20},CoefficientList[Series[1/(2-x-Exp[3x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 16 2024 *)
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 3^j*binomial(i, j)*v[i-j+1])); v;
A367847
Expansion of e.g.f. 1/(1 - x + log(1 - 4*x)).
Original entry on oeis.org
1, 5, 66, 1358, 37592, 1304536, 54384080, 2646247152, 147186205056, 9210766696320, 640472632680192, 48989958019395840, 4087959251421060096, 369547591764702870528, 35976590549993421907968, 3752609987262290143082496, 417518648351593243448279040
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 4^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
A367840
Expansion of e.g.f. 1/(2 + x - exp(4*x)).
Original entry on oeis.org
1, 3, 34, 514, 10456, 265704, 8103120, 288302480, 11722944896, 536262671488, 27256865214208, 1523936708699904, 92949383868668928, 6141694449341637632, 437033351625771001856, 33319937543640487708672, 2709708041047388536274944
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-i*v[i]+sum(j=1, i, 4^j*binomial(i, j)*v[i-j+1])); v;
Showing 1-4 of 4 results.