A357966
Expansion of e.g.f. exp( x * (exp(x^2) - 1) ).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 360, 840, 20160, 75600, 1058400, 10311840, 79833600, 1305944640, 11018367360, 174616041600, 2150397849600, 28661419987200, 473667677683200, 6293779652160000, 114484773731328000, 1766543101087564800, 31640707215390873600
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2)-1))))
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a(n) = n!*sum(k=0, n\2, stirling(k, n-2*k, 2)/k!);
A375561
Expansion of e.g.f. 1 / (1 + x * log(1 - x^2)).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 720, 1680, 40320, 453600, 3326400, 67858560, 878169600, 11935123200, 240708948480, 3946374432000, 73927190937600, 1621341859737600, 32960791774310400, 758085507686707200, 18570669277095936000, 454016684061997056000, 12100759898595611443200
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2))))
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a(n) = n!*sum(k=0, n\2, (n-2*k)!*abs(stirling(k, n-2*k, 1))/k!);
A353227
Expansion of e.g.f. (1 - x^3)^(-x).
Original entry on oeis.org
1, 0, 0, 0, 24, 0, 0, 2520, 20160, 0, 1209600, 19958400, 79833600, 1556755200, 39956716800, 326918592000, 5056340889600, 148203095040000, 1867358997504000, 30411275102208000, 946128558735360000, 15965919428659200000, 293266062902292480000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^3)^(-x)))
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*log(1-x^3))))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, (i+2)\3, (3*j-2)/(j-1)*v[i-3*j+3]/(i-3*j+2)!)); v;
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a(n) = n!*sum(k=0, n\3, abs(stirling(k, n-3*k, 1))/k!);
A351155
Expansion of e.g.f. (1 - x^2/2)^(-x).
Original entry on oeis.org
1, 0, 0, 3, 0, 15, 90, 210, 2520, 13230, 103950, 873180, 7484400, 72972900, 745404660, 8185126950, 95805309600, 1184852869200, 15538995271800, 214159261516200, 3109622647131000, 47252530639314000, 752635500963746400, 12499951421009052000, 216709136059079664000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^2/2)^(-x)))
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*log(1-x^2/2))))
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, (i+1)\2, (2*j-1)/((j-1)*2^(j-1))*v[i-2*j+2]/(i-2*j+1)!)); v;
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a(n) = n!*sum(k=0, n\2, abs(stirling(k, n-2*k, 1))/(2^k*k!));
A376350
E.g.f. satisfies A(x) = 1/(1 - x^2*A(x)^2)^(x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 2520, 1680, 181440, 6138720, 18295200, 1444988160, 46443196800, 357015859200, 25016537145600, 818965321574400, 12259854032025600, 815066633667686400, 28461465853402982400, 691667282863484928000, 45198900807076912896000, 1739192274792359202816000, 60318174486002275287244800
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2)^x)/x))
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a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*abs(stirling(k, n-2*k, 1))/k!);
Showing 1-5 of 5 results.