A370508
Expansion of Sum_{k>=0} k! * ( x * (1-x^3) )^k.
Original entry on oeis.org
1, 1, 2, 6, 23, 116, 702, 4944, 39722, 358578, 3593664, 39595440, 475746474, 6190838544, 86740334160, 1301939398080, 20842001737224, 354469125185880, 6382790173842480, 121310821042966800, 2426863248540057480, 50975836645480342560, 1121691979824460425360
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1-x^3))^k))
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a(n) = sum(k=0, n\4, (-1)^k*(n-3*k)!*binomial(n-3*k, k));
A370509
Expansion of Sum_{k>=0} k! * ( x * (1+x^2) )^k.
Original entry on oeis.org
1, 1, 2, 7, 28, 138, 818, 5658, 44784, 399366, 3962256, 43289760, 516432984, 6679346280, 93091875120, 1390851720840, 22175338353120, 375794883339120, 6745177713093840, 127830886641354960, 2550687440585679360, 53451172032327664560, 1173650135526055272960
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1+x^2))^k))
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a(n) = sum(k=0, n\3, (n-2*k)!*binomial(n-2*k, k));
A370668
Expansion of Sum_{k>0} k! * ( x * (1+x^k) )^k.
Original entry on oeis.org
1, 3, 6, 28, 120, 740, 5040, 40416, 362898, 3629400, 39916800, 479006070, 6227020800, 87178326480, 1307674369200, 20922790210656, 355687428096000, 6402373709004720, 121645100408832000, 2432902008212929224, 51090942171709545840, 1124000727778046764800
Offset: 1
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my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*(x*(1+x^k))^k))
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a(n) = sumdiv(n,d, d!*binomial(d, n/d-1));
Showing 1-3 of 3 results.