A358065
Expansion of e.g.f. 1/(1 - x * exp(x^3)).
Original entry on oeis.org
1, 1, 2, 6, 48, 360, 2880, 27720, 322560, 4173120, 58665600, 911433600, 15567552000, 287740252800, 5710178073600, 121450256928000, 2758495490150400, 66563938106265600, 1699990278213427200, 45828946821385728000, 1300703752243703808000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^3))))
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a(n) = n!*sum(k=0, n\3, (n-3*k)^k/k!);
A356629
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(n - 3*k)!.
Original entry on oeis.org
1, 1, 1, 1, 25, 121, 361, 5881, 82321, 547345, 6053041, 167991121, 2179469161, 22892967241, 788375451865, 18046198202761, 245523704069281, 7548055281543841, 270833271588545761, 5369819950838359585, 141456920470310708281, 6760255576117937586841
Offset: 0
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a[n_] := n! * Sum[(n - 3*k)^k/(n - 3*k)!, {k, 0, Floor[n/3]}]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 19 2022 *)
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a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(n-3*k)!);
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^3)))))
A354554
Expansion of e.g.f. exp( x * exp(x^4) ).
Original entry on oeis.org
1, 1, 1, 1, 1, 121, 721, 2521, 6721, 196561, 3659041, 29993041, 159762241, 1686639241, 60298558321, 987112886761, 9315623640961, 76611297104161, 2454331471018561, 69805324167893281, 1086439146068753281, 11530308934656915481
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^4)))))
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a(n) = n!*sum(k=0, n\4, (n-4*k)^k/(k!*(n-4*k)!));
A367719
E.g.f. satisfies A(x) = exp(x*A(x^3)).
Original entry on oeis.org
1, 1, 1, 1, 25, 121, 361, 3361, 42001, 275185, 1819441, 30777121, 371238121, 9284332201, 131442054745, 1454933712961, 34120902859681, 851562584890081, 12300037440760801, 187928965721651905, 6019555345508794681, 130768735411230580441
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-1)!*sum(j=0, (i-1)\3, (3*j+1)*v[j+1]*v[i-3*j]/(j!*(i-1-3*j)!))); v;
A358063
Expansion of e.g.f. exp( x * exp(-x^3) ).
Original entry on oeis.org
1, 1, 1, 1, -23, -119, -359, 1681, 38641, 269137, 599761, -22461119, -347288039, -2477852519, 13993475497, 670329026641, 8887630708321, 29011883003041, -1682765787379679, -40673626173010943, -409560067877703479, 4061870252008891561, 235100528524188216121
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-x^3))))
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a(n) = n!*sum(k=0, n\3, (-n+3*k)^k/(k!*(n-3*k)!));
A362655
E.g.f. satisfies A(x) = exp( x * exp(x^3) * A(x) ).
Original entry on oeis.org
1, 1, 3, 16, 149, 1656, 22567, 369664, 7081209, 155178928, 3830958251, 105267080304, 3187172910517, 105437661606616, 3784329536385231, 146474021771040856, 6081955388047685873, 269686446704697314016, 12719466142269818201299
Offset: 0
Showing 1-6 of 6 results.
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