A372315
Expansion of e.g.f. exp( x - LambertW(-2*x)/2 ).
Original entry on oeis.org
1, 2, 8, 68, 960, 18832, 471136, 14324480, 512733696, 21119803136, 984029612544, 51169331031040, 2937675286583296, 184560174104465408, 12594824112085327872, 927757127285523243008, 73369903633161123397632, 6200198958236463387836416
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));
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));
A372334
Expansion of e.g.f. -exp(x) * LambertW(-3*x)/3.
Original entry on oeis.org
0, 1, 8, 102, 2092, 60140, 2220954, 100119670, 5328468968, 326960686872, 22724388453070, 1764411577328906, 151364204180518476, 14217940294767407380, 1451334877597451677250, 159972528561402504191190, 18936257811933773637390544, 2395818853376147403857700656
Offset: 0
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-exp(x)*lambertw(-3*x)/3)))
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a(n) = sum(k=1, n, (3*k)^(k-1)*binomial(n, k));
Showing 1-4 of 4 results.