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)))))
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)))))
A356668
Expansion of e.g.f. Sum_{k>=0} x^k / (k! - k*x^k).
Original entry on oeis.org
1, 1, 3, 7, 37, 121, 1141, 5041, 60761, 378001, 5444461, 39916801, 729041545, 6227020801, 130767460825, 1321314894901, 31388220966961, 355687428096001, 9636906872926477, 121645100408832001, 3649432697160095561, 51223991519836175041, 1686001091666419279753
Offset: 0
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a[n_]:= n! * DivisorSum[n, 1/(# * (# - 1)!^(n/#)) &]; a[0] = 1; Array[a, 23, 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/(k!-k*x^k))))
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a(n) = if(n==0, 1, n!*sumdiv(n, d, 1/(d*(d-1)!^(n/d))));
Showing 1-3 of 3 results.