A353226
Expansion of e.g.f. (1 - x^2)^(-x).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 360, 1680, 20160, 151200, 1663200, 17962560, 219542400, 2854051200, 40441040640, 606356150400, 9793028044800, 166481476761600, 3017626733721600, 57359043873331200, 1153275200453376000, 24233844054131712000, 535361100608439705600
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^2)^(-x)))
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*log(1-x^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)*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))/k!);
A357967
Expansion of e.g.f. exp( x * (exp(x^3) - 1) ).
Original entry on oeis.org
1, 0, 0, 0, 24, 0, 0, 2520, 20160, 0, 604800, 19958400, 79833600, 259459200, 25427001600, 326918592000, 1046139494400, 44460928512000, 1333827855360000, 10306043229081600, 125024130975744000, 6386367771463680000, 101695303941783552000, 861733891296165888000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3)-1))))
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a(n) = n!*sum(k=0, n\3, stirling(k, n-3*k, 2)/k!);
A351156
Expansion of e.g.f. (1 - x^3/6)^(-x).
Original entry on oeis.org
1, 0, 0, 0, 4, 0, 0, 70, 560, 0, 5600, 92400, 369600, 1201200, 30830800, 252252000, 1210809600, 19059040000, 240143904000, 1738184448000, 22451549120000, 342205063200000, 3417705170880000, 43866126368064000, 732641268463104000, 9234973972224000000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^3/6)^(-x)))
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*log(1-x^3/6))))
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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)*6^(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))/(6^k*k!));
A375562
Expansion of e.g.f. 1 / (1 + x * log(1 - x^3)).
Original entry on oeis.org
1, 0, 0, 0, 24, 0, 0, 2520, 40320, 0, 1209600, 39916800, 479001600, 1556755200, 79913433600, 1961511552000, 25107347865600, 296406190080000, 11204153985024000, 263564384219136000, 4284610758844416000, 95795516571955200000, 3345240261242880000000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^3))))
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a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(k, n-3*k, 1))/k!);
Showing 1-4 of 4 results.