A352304
Expansion of e.g.f. 1/(exp(x) - x^4).
Original entry on oeis.org
1, -1, 1, -1, 25, -241, 1441, -6721, 67201, -1185409, 16652161, -180639361, 2098673281, -37526586241, 785718950017, -14516030954881, 247504017895681, -4832929862019841, 116556246644716801, -2930255897793414913, 69746855593499124481, -1673960044278244020481
Offset: 0
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m = 21; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^4), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)
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my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-x^4)))
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b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 4);
A352299
Expansion of e.g.f. 1/(2 - exp(x) - x^3).
Original entry on oeis.org
1, 1, 3, 19, 123, 1021, 10683, 127093, 1725867, 26535613, 452307243, 8475606613, 173390108235, 3842119808749, 91675559886459, 2343875745873493, 63920729617231275, 1852126733351677021, 56823327291638414667, 1840195730889731550805
Offset: 0
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m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^3), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^3)))
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b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 3);
A352302
Expansion of e.g.f. 1/(exp(x) - x^2).
Original entry on oeis.org
1, -1, 3, -13, 73, -521, 4441, -44185, 502545, -6429169, 91393201, -1429101521, 24378097129, -450504733849, 8965682806809, -191174795868841, 4348171177591201, -105077942935229537, 2688685949077138657, -72618903735812907553, 2064598911185525708601
Offset: 0
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m = 20; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^2), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)
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my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-x^2)))
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b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 2);
A352310
Expansion of e.g.f. 1/(exp(x) - x^3/6).
Original entry on oeis.org
1, -1, 1, 0, -7, 39, -139, 139, 3249, -38305, 257641, -724681, -9925519, 208718223, -2209932451, 11619569779, 98841199521, -3691083087521, 56488651405393, -466578080641297, -1989509977776479, 159427986446212959, -3372599255892634459, 39809520784433784075
Offset: 0
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m = 23; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^3/6), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)
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my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-x^3/6)))
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b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m))*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 3);
A375610
Expansion of e.g.f. 1 / (exp(-x) - x^3).
Original entry on oeis.org
1, 1, 1, 7, 49, 241, 1681, 18481, 192193, 2028097, 26854561, 400419361, 6074016961, 100260498625, 1847840462833, 36061045391281, 738757221740161, 16244778936351361, 380460397886975809, 9341152506044172865, 241084169507148900481, 6559259107807215358081
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x)-x^3)))
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a(n) = n!*sum(k=0, n\3, (k+1)^(n-3*k)/(n-3*k)!);
Showing 1-5 of 5 results.