A356628
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(n - 2*k)!.
Original entry on oeis.org
1, 1, 1, 7, 25, 181, 1561, 12811, 188497, 2071945, 38889361, 620762671, 12917838121, 291278938237, 6667342764265, 194869722610291, 5137978752994081, 177509783765281681, 5610285632192738977, 215195998789004395735, 8228064506323330305721
Offset: 0
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a[n_] := n! * Sum[(n - 2*k)^k/(n - 2*k)!, {k, 0, Floor[n/2]}]; a[0] = 1; Array[a, 21, 0] (* Amiram Eldar, Aug 19 2022 *)
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a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(n-2*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^2)))))
A356673
a(n) = n! * Sum_{k=0..n} k^(3*(n-k))/k!.
Original entry on oeis.org
1, 1, 3, 31, 901, 45741, 3960871, 584698843, 130554106761, 40790044059481, 17681098707667531, 10491554658622447191, 8198225417359164798733, 8172446419302496167191941, 10264848632098736708582150511
Offset: 0
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a(n) = n!*sum(k=0, n, k^(3*(n-k))/k!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k^3*x)))))
A356328
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(6^k * (n - 3*k)!).
Original entry on oeis.org
1, 1, 1, 1, 5, 21, 61, 281, 2521, 15625, 84841, 971521, 10646461, 83366141, 962405445, 15445935961, 181502928881, 2182235585041, 42297481449361, 714940186390465, 10007476059187381, 204722588272279141, 4600003555996715021, 80767827313930590681
Offset: 0
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a[n_] := n! * Sum[(n - 3*k)^k/(6^k*(n - 3*k)!), {k, 0, Floor[n/3]}]; a[0] = 1; Array[a, 24, 0] (* Amiram Eldar, Aug 19 2022 *)
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a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^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^3/6)))))
A356630
a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(n - 4*k)!.
Original entry on oeis.org
1, 1, 1, 1, 1, 121, 721, 2521, 6721, 378001, 7287841, 59930641, 319429441, 7524471241, 353072319601, 5897248517161, 55827317669761, 726274560953761, 53139878190826561, 1650487849152976801, 25981849479032542081, 317292238756098973081
Offset: 0
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a[n_] := n! * Sum[(n - 4*k)^k/(n - 4*k)!, {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 19 2022 *)
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a(n) = n!*sum(k=0, n\4, (n-4*k)^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)))))
A357147
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^(3*k)/(n - 3*k)!.
Original entry on oeis.org
1, 1, 1, 1, 25, 481, 3241, 18481, 1332241, 44198785, 623190961, 15416707681, 1602405014761, 68167258954081, 1598025440555545, 134130467333575441, 14793638741719612321, 730659540435131811841, 34674365632872552887521, 5776415685538277157146305
Offset: 0
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a(n) = n!*sum(k=0, n\3, (n-3*k)^(3*k)/(n-3*k)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-(k*x)^3)))))
Showing 1-5 of 5 results.