A375587
Expansion of e.g.f. 1 / (1 + x - x * exp(x^3/6)).
Original entry on oeis.org
1, 0, 0, 0, 4, 0, 0, 70, 1120, 0, 2800, 184800, 2217600, 200200, 39239200, 1513512000, 16166550400, 11435424000, 1029188160000, 31290941281600, 317363510464000, 821292151680000, 52198475641312000, 1387554839326656000, 14092570281613824000, 92349968764253200000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^3/6))))
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a(n) = n!*sum(k=0, n\3, (n-3*k)!*stirling(k, n-3*k, 2)/(6^k*k!));
A375589
Expansion of e.g.f. 1 / (1 + x - x * exp(x^3)).
Original entry on oeis.org
1, 0, 0, 0, 24, 0, 0, 2520, 40320, 0, 604800, 39916800, 479001600, 259459200, 50854003200, 1961511552000, 21097146470400, 88921857024000, 8002967132160000, 243459152346009600, 2642401903325184000, 38318206628782080000, 2435557926202232832000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^3))))
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a(n) = n!*sum(k=0, n\3, (n-3*k)!*stirling(k, n-3*k, 2)/k!);
A367885
Expansion of e.g.f. 1/(1 - x * (exp(2*x) - 1)).
Original entry on oeis.org
1, 0, 4, 12, 128, 1040, 12672, 161728, 2481152, 41806080, 791613440, 16399944704, 371591995392, 9110211874816, 240670782291968, 6810264853463040, 205583847590985728, 6593508525460226048, 223913466256013918208, 8026367531323488993280
Offset: 0
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a(n) = n!*sum(k=0, n\2, 2^(n-k)*k!*stirling(n-k, k, 2)/(n-k)!);
A367886
Expansion of e.g.f. 1/(1 - x * (exp(3*x) - 1)).
Original entry on oeis.org
1, 0, 6, 27, 324, 3645, 54918, 923643, 18061704, 394663833, 9607469130, 256997250279, 7502660832780, 237243300445125, 8079508278302958, 294800526215739315, 11473728720705019152, 474469344621574172721, 20774758472643152149650
Offset: 0
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a(n) = n!*sum(k=0, n\2, 3^(n-k)*k!*stirling(n-k, k, 2)/(n-k)!);
A375683
Expansion of e.g.f. 1 / (1 + x * (exp(x) - 1)).
Original entry on oeis.org
1, 0, -2, -3, 20, 115, -306, -6307, -6616, 462663, 2956130, -38945951, -656504388, 2325876683, 145820995670, 562691968005, -33452317341616, -449954883966065, 7055017491780810, 233802046526955497, -571834988279277340, -112474674691684827501
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*(exp(x)-1))))
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a(n) = n!*sum(k=0, n\2, (-1)^k*k!*stirling(n-k, k, 2)/(n-k)!);
A220222
Triangular array read by rows. T(n,k) is the number of functional digraphs on {1,2,...,n} such that no node is at a distance greater than one from a cycle and there are k recurrent elements whose preimage contains only one element, n>=0, 0<=k<=n.
Original entry on oeis.org
1, 0, 1, 2, 0, 2, 3, 12, 0, 6, 28, 24, 72, 0, 24, 125, 400, 180, 480, 0, 120, 1146, 2220, 4680, 1440, 3600, 0, 720, 8827, 29064, 30870, 53760, 12600, 30240, 0, 5040, 94200, 272272, 545328, 409920, 638400, 120960, 282240, 0, 40320, 1007001, 3722688, 5989032, 9386496, 5518800, 7983360, 1270080, 2903040, 0, 362880
Offset: 0
1,
0, 1,
2, 0, 2,
3, 12, 0, 6,
28, 24, 72, 0, 24,
125, 400, 180, 480, 0, 120, 0
1146, 2220, 4680, 1440, 3600, 0, 720
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nn=6;a=x Exp[x];Range[0,nn]!CoefficientList[Series[1/(1-x (Exp[x]-1+y)),{x,0,nn}],{x,y}]//Grid
A355666
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 - x^k/k! * (exp(x) - 1)).
Original entry on oeis.org
1, 1, 1, 1, 0, 3, 1, 0, 2, 13, 1, 0, 0, 3, 75, 1, 0, 0, 3, 28, 541, 1, 0, 0, 0, 6, 125, 4683, 1, 0, 0, 0, 4, 10, 1146, 47293, 1, 0, 0, 0, 0, 10, 195, 8827, 545835, 1, 0, 0, 0, 0, 5, 20, 1281, 94200, 7087261, 1, 0, 0, 0, 0, 0, 15, 35, 5908, 1007001, 102247563, 1, 0, 0, 0, 0, 0, 6, 35, 1176, 68076, 12814390, 1622632573
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 0, 0, 0, 0, 0, 0, ...
3, 2, 0, 0, 0, 0, 0, ...
13, 3, 3, 0, 0, 0, 0, ...
75, 28, 6, 4, 0, 0, 0, ...
541, 125, 10, 10, 5, 0, 0, ...
4683, 1146, 195, 20, 15, 6, 0, ...
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T(n, k) = n!*sum(j=0, n\(k+1), j!*stirling(n-k*j, j, 2)/(k!^j*(n-k*j)!));
Comments