A372316
Expansion of e.g.f. exp( x - LambertW(-3*x)/3 ).
Original entry on oeis.org
1, 2, 10, 125, 2644, 77597, 2904382, 132169403, 7083715240, 437031850841, 30506442905194, 2377038378159359, 204521399708464252, 19259006462435865413, 1970114326513629358654, 217556451608123850352523, 25794252755430105917806288, 3268152272130255473300883377
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x)/3)))
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a(n) = sum(k=0, n, (3*k+1)^(k-1)*binomial(n, k));
A372320
Expansion of e.g.f. -exp( x + LambertW(-2*x)/2 ).
Original entry on oeis.org
-1, 0, 4, 36, 464, 8560, 206112, 6104896, 214376192, 8701657344, 400748710400, 20642974511104, 1175888936749056, 73389707156586496, 4980134850525986816, 365062349226075463680, 28747688571714736160768, 2420266280392895064506368
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x+lambertw(-2*x)/2)))
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a(n) = sum(k=0, n, (2*k-1)^(k-1)*binomial(n, k));
A372321
Expansion of e.g.f. -exp( x + LambertW(-3*x)/3 ).
Original entry on oeis.org
-1, 0, 6, 81, 1620, 45765, 1671678, 74794671, 3958829640, 241898775273, 16756621904970, 1297547591499819, 111065107263415308, 10412999996499836541, 1061234184094567585326, 116812280111404106348415, 13810631408232372091755792, 1745470697932523785587735249
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x+lambertw(-3*x)/3)))
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a(n) = sum(k=0, n, (3*k-1)^(k-1)*binomial(n, k));
A372333
Expansion of e.g.f. -exp(x) * LambertW(-2*x)/2.
Original entry on oeis.org
0, 1, 6, 51, 684, 12965, 317298, 9500631, 336237016, 13729172553, 635237632350, 32844916975739, 1876755685038468, 117437155609780461, 7986793018367861194, 586578825469711599135, 46268265552518066488752, 3901008402618593931019409
Offset: 0
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-exp(x)*lambertw(-2*x)/2)))
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a(n) = sum(k=1, n, (2*k)^(k-1)*binomial(n, k));
Showing 1-4 of 4 results.