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;
A367845
Expansion of e.g.f. 1/(1 - x + log(1 - 2*x)).
Original entry on oeis.org
1, 3, 22, 250, 3816, 72968, 1675568, 44901456, 1375306368, 47392683648, 1814635323648, 76430014409472, 3511792144942080, 174806087920727040, 9370642040786049024, 538202280800536799232, 32972397141008692445184, 2146270648672407967137792
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, 2^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
A367837
Expansion of e.g.f. 1/(2 - x - exp(4*x)).
Original entry on oeis.org
1, 5, 66, 1294, 33752, 1100504, 43060176, 1965653232, 102548623744, 6018735869824, 392498702352128, 28155539333730560, 2203322337542003712, 186790304541786160128, 17053569926181643921408, 1668166923908523824576512, 174057374767036007615922176
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;
A367830
E.g.f. A(x) satisfies A(x) = (1 + (exp(x) - 1) * A(2*x)) / (1 - x).
Original entry on oeis.org
1, 2, 13, 208, 7817, 681626, 136872113, 62739300968, 64993463748977, 150619722938940622, 773428868899900772345, 8724654696222415759129388, 214574098061440421518595200025, 11429824974654804201081062775335234, 1311103770238649103823410558613476172193
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, 2^(i-j)*binomial(i, j)*v[i-j+1])); v;
A367838
Expansion of e.g.f. 1/(2 + x - exp(2*x)).
Original entry on oeis.org
1, 1, 6, 38, 344, 3832, 51408, 803952, 14371456, 289005440, 6457624832, 158719896832, 4255775425536, 123619815742464, 3867071262472192, 129610289219999744, 4633674344869756928, 176011269522607144960, 7079115958438736363520
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, 2^j*binomial(i, j)*v[i-j+1])); v;
A367924
Expansion of e.g.f. 1/(3 - x - 2*exp(x)).
Original entry on oeis.org
1, 3, 20, 200, 2666, 44422, 888214, 20719722, 552385386, 16567346630, 552104425070, 20238679934002, 809341290336274, 35062535546332062, 1635835480858764342, 81770970437144725034, 4360009179878123161658, 247004345719314584973430
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]+2*sum(j=1, i, binomial(i, j)*v[i-j+1])); v;
Showing 1-6 of 6 results.