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)))))
A345747
a(n) = n! * Sum_{k=0..floor(n/2)} k^(n - 2*k)/k!.
Original entry on oeis.org
1, 0, 2, 6, 36, 240, 2280, 27720, 425040, 7862400, 171188640, 4319330400, 125199708480, 4142318019840, 155388782989440, 6557345831836800, 308677784640825600, 16079233115648102400, 920518264903690252800, 57603377545940850624000
Offset: 0
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Join[{1}, Table[n!*Sum[k^(n - 2*k)/k!, {k, 0, n/2}], {n, 1, 20}]] (* Vaclav Kotesovec, Oct 30 2022 *)
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a(n) = n!*sum(k=0, n\2, k^(n-2*k)/k!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^(2*k)/(k!*(1-k*x)))))
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)))))
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)))))
A356672
a(n) = n! * Sum_{k=0..n} k^(2*(n-k))/k!.
Original entry on oeis.org
1, 1, 3, 19, 253, 5661, 188191, 8983423, 594848409, 52174034713, 5852229698971, 822684190381131, 142739480367287893, 30074750245383836149, 7575373641076070706423, 2252600759590927171373431, 783103569459739402827046321, 315587346190678252431713684913
Offset: 0
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a(n) = n!*sum(k=0, n, k^(2*(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^2*x)))))
A357146
a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^(2*k)/(n - 2*k)!.
Original entry on oeis.org
1, 1, 1, 7, 49, 301, 6241, 74131, 1722337, 46346329, 1090339201, 48905462431, 1584330498961, 81705172522117, 4191355357015009, 223743062044497451, 16563314120270608321, 1027165911865738200241, 91346158358120706564097, 7395168869747626389974839
Offset: 0
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a(n) = n!*sum(k=0, n\2, (n-2*k)^(2*k)/(n-2*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)^2)))))
Showing 1-6 of 6 results.