A371370
E.g.f. satisfies A(x) = -log(1 - x/(1 - A(x))^2).
Original entry on oeis.org
0, 1, 5, 62, 1246, 34734, 1239708, 53958456, 2771832656, 164151829440, 11010949643640, 825134834757936, 68321156113803360, 6194283782068848816, 610322188305019432032, 64936303681095948453120, 7419917758371561069774336, 906217650382400588573066880
Offset: 0
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Table[Sum[(2*n+k-2)!/(2*n-1)! * Abs[StirlingS1[n,k]], {k,1,n}], {n,0,20}] (* Vaclav Kotesovec, Sep 10 2024 *)
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^2*(1-exp(-x))))))
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a(n) = sum(k=1, n, (2*n+k-2)!/(2*n-1)!*abs(stirling(n, k, 1)));
A376037
E.g.f. satisfies A(x) = (exp(x / (1 - A(x))^2) - 1) / (1 - A(x)).
Original entry on oeis.org
0, 1, 7, 115, 3047, 111771, 5244555, 299941195, 20239069807, 1574068019851, 138641219870243, 13640672949173403, 1482772864485867399, 176478769995088245595, 22825571074271407363771, 3187825736999237502879019, 478120273969744650293424095
Offset: 0
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a(n) = sum(k=1, n, (2*n+2*k-2)!/(2*n+k-1)!*stirling(n, k, 2));
A368033
E.g.f. satisfies A(x) = log(1 + x/(1 - A(x))^2).
Original entry on oeis.org
0, 1, 3, 26, 370, 7334, 186468, 5787144, 212100208, 8964974016, 429304991880, 22971063265776, 1358260804832160, 87949592273821680, 6189420503357272608, 470384337802047909120, 38393707193347187344896, 3349704214386311986028160
Offset: 0
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^2*(exp(x)-1)))))
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a(n) = sum(k=1, n, (2*n+k-2)!/(2*n-1)!*stirling(n, k, 1));
A376035
E.g.f. satisfies A(x) = exp(x / (1 - A(x))^3) - 1.
Original entry on oeis.org
0, 1, 7, 118, 3205, 120466, 5790619, 339216046, 23443311049, 1867308836986, 168435092561671, 16971155810393302, 1889194092179682061, 230257485553145337106, 30496977601634473249363, 4361533380688447142658046, 669865656003334085318195089
Offset: 0
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Table[Sum[(3*n+k-2)!/(3*n-1)! * StirlingS2[n,k], {k,1,n}], {n,0,20}] (* Vaclav Kotesovec, Sep 10 2024 *)
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^3*log(1+x)))))
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a(n) = sum(k=1, n, (3*n+k-2)!/(3*n-1)!*stirling(n, k, 2));
Showing 1-4 of 4 results.