A356632
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/2^k.
Original entry on oeis.org
1, 1, 2, 9, 48, 330, 2880, 29610, 362880, 5148360, 83462400, 1535549400, 31614105600, 724183059600, 18307441152000, 507367438578000, 15336404987904000, 502812808754256000, 17805001275629568000, 678167395781763888000, 27681559049033809920000
Offset: 0
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a[n_] := n! * Sum[(n - 2*k)^k/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/2^k);
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^2/2))))
A356633
a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/6^k.
Original entry on oeis.org
1, 1, 2, 6, 28, 160, 1080, 8540, 78400, 816480, 9492000, 122337600, 1736380800, 26930904000, 453515462400, 8254694448000, 161734564992000, 3397235761920000, 76228261933824000, 1821644243362944000, 46233794313907200000, 1242946827521118720000
Offset: 0
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a[n_] := n! * Sum[(n - 3*k)^k/6^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/6^k);
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^3/6))))
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)))))
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)))))
A356667
Expansion of e.g.f. Sum_{k>=0} x^k / (1 - k*x^k/k!).
Original entry on oeis.org
1, 1, 4, 12, 72, 240, 2520, 10080, 127680, 816480, 11037600, 79833600, 1514177280, 12454041600, 261655954560, 2699348652000, 62869385779200, 711374856192000, 19407798693803520, 243290200817664000, 7300765959334848000, 102980278869910041600
Offset: 0
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a[n_]:= n! * DivisorSum[n, 1/(# - 1)!^(n/# - 1) &]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 22 2022 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^k/k!))))
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a(n) = if(n==0, 1, n!*sumdiv(n, d, 1/(d-1)!^(n/d-1)));
Showing 1-5 of 5 results.