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)))))
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))))
A356634
a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/24^k.
Original entry on oeis.org
1, 1, 2, 6, 24, 125, 780, 5670, 47040, 439110, 4561200, 52182900, 651974400, 8832874050, 129001672800, 2020822303500, 33805804032000, 601587281295000, 11348960759136000, 226275153994890000, 4755046903326720000, 105061084389756495000, 2435176811445618240000
Offset: 0
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a[n_] := n! * Sum[(n - 4*k)^k/24^k, {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 23, 0] (* Amiram Eldar, Aug 19 2022 *)
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a(n) = n!*sum(k=0, n\4, (n-4*k)^k/24^k);
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^4/24))))
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)))))
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.