A353546
Expansion of e.g.f. -log(1-2*x) * exp(x)/2.
Original entry on oeis.org
0, 1, 4, 17, 96, 729, 7060, 83033, 1146656, 18164625, 324488068, 6450956929, 141233271872, 3376008830505, 87480173354964, 2442396780039817, 73089894980585408, 2333809837398044321, 79198287879591647364, 2846319497398561356913
Offset: 0
Essentially partial sums of
A010844.
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-2*x)*exp(x)/2)))
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a(n) = n!*sum(k=0, n-1, 2^(n-1-k)/((n-k)*k!));
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a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(2*i-1)*v[i]-2*(i-1)*v[i-1]+1); v;
A353548
Expansion of e.g.f. -log(1-4*x) * exp(x)/4.
Original entry on oeis.org
0, 1, 6, 47, 540, 8429, 166210, 3952955, 109981816, 3502905369, 125648153278, 5011458069639, 219987094389524, 10538817637744005, 547118005892177018, 30595552548140425747, 1833501625083035349488, 117219490267316310468913
Offset: 0
Essentially partial sums of
A056545.
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-4*x)*exp(x)/4)))
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a(n) = n!*sum(k=0, n-1, 4^(n-1-k)/((n-k)*k!));
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a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(4*i-3)*v[i]-4*(i-1)*v[i-1]+1); v;
A353549
Expansion of e.g.f. log(1+3*x) * exp(x)/3.
Original entry on oeis.org
0, 1, -1, 12, -104, 1289, -19605, 356488, -7541464, 182009385, -4935863537, 148600324124, -4918093868688, 177482897072545, -6936155749635541, 291836667412104072, -13152940374866178512, 632196357654491385521, -32280617841842744380161
Offset: 0
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(log(1+3*x)*exp(x)/3)))
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a(n) = n!*sum(k=0, n-1, (-3)^(n-1-k)/((n-k)*k!));
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a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(-3*i+4)*v[i]+3*(i-1)*v[i-1]+1); v;
A354419
Expansion of e.g.f. log(1+4*x) * exp(x)/4.
Original entry on oeis.org
0, 1, -2, 23, -276, 4509, -91190, 2205587, -62104168, 1995807993, -72089029802, 2891304481999, -127498010037244, 6131189086886421, -319320539953144158, 17905976286288568267, -1075611833288214177232, 68909527979479961534705
Offset: 0
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(log(1+4*x)*exp(x)/4)))
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a(n) = n!*sum(k=0, n-1, (-4)^(n-1-k)/((n-k)*k!));
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a_vector(n) = my(v=vector(n+1, i, if(i==2, 1, 0))); for(i=2, n, v[i+1]=(-4*i+5)*v[i]+4*(i-1)*v[i-1]+1); v;
Showing 1-4 of 4 results.