A354550
Expansion of e.g.f. exp( x * exp(x^2/2) ).
Original entry on oeis.org
1, 1, 1, 4, 13, 46, 241, 1156, 6889, 44668, 300241, 2328976, 18390901, 159273544, 1461200833, 13995753136, 144068872081, 1531949061136, 17259159775969, 202543867724608, 2474236899786781, 31633380519660256, 417760492214548561, 5751414293905728064
Offset: 0
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With[{nn=30},CoefficientList[Series[Exp[x Exp[x^2/2]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 03 2024 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2/2)))))
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a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!*(n-2*k)!));
A354551
Expansion of e.g.f. exp( x * exp(x^3/6) ).
Original entry on oeis.org
1, 1, 1, 1, 5, 21, 61, 211, 1401, 8065, 37241, 240021, 1997821, 13856701, 94418325, 874328911, 8304303281, 69158458881, 658339599601, 7454839614985, 78224066633781, 805961931388741, 9828080719704941, 124199805022959051, 1466207770078872745
Offset: 0
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With[{nn=30},CoefficientList[Series[Exp[x*Exp[x^3/6]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 03 2025 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3/6)))))
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a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^k*k!*(n-3*k)!));
A356608
a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(24^k * (n - 4*k)!).
Original entry on oeis.org
1, 1, 1, 1, 1, 6, 31, 106, 281, 1261, 13861, 106261, 558361, 2709136, 32802771, 447762316, 4093711441, 28011714641, 293624974441, 5549250905281, 80454378591121, 815886496908946, 8379058314620071, 168672787637953446, 3514729162490432041, 51656083670790267901
Offset: 0
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a[n_] := n! * Sum[(n - 4*k)^k/(24^k*(n - 4*k)!), {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 26, 0] (* Amiram Eldar, Aug 19 2022 *)
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a(n) = n!*sum(k=0, n\4, (n-4*k)^k/(24^k*(n-4*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^4/24)))))
Showing 1-3 of 3 results.
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