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)))))
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))))
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))))
A356029
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * (n - 2*k)!).
Original entry on oeis.org
1, 1, 1, 4, 13, 61, 421, 2626, 27049, 245953, 3069721, 40222216, 576988501, 10058716669, 169773404893, 3596206855606, 73450508303761, 1775382487932001, 43993288886533489, 1183551336464017708, 34806599282992709341, 1043452963148195577181
Offset: 0
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a[n_] := n! * Sum[(n - 2*k)^k/(2^k*(n - 2*k)!), {k, 0, Floor[n/2]}]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 19 2022 *)
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a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^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^2/2)))))
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.