A375556
Expansion of e.g.f. 1 / (1 + x * log(1 - x^3/6)).
Original entry on oeis.org
1, 0, 0, 0, 4, 0, 0, 70, 1120, 0, 5600, 184800, 2217600, 1201200, 61661600, 1513512000, 16682265600, 38118080000, 1440863424000, 31721866176000, 352561745536000, 2053230379200000, 68832104140800000, 1449890913639168000, 17583390443114496000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^3/6))))
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a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(k, n-3*k, 1))/(6^k*k!));
A375237
Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^2.
Original entry on oeis.org
1, 0, 0, 6, 0, 30, 540, 420, 15120, 192780, 623700, 15467760, 187110000, 1394593200, 30353483160, 401350950000, 4974611241600, 105201040744800, 1624218256861200, 27525899782180800, 599214125325816000, 10967831645346576000, 227431647445400798400
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2/2))^2))
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*abs(stirling(k, n-2*k, 1))/(2^k*k!));
A375558
Expansion of e.g.f. 1 / (1 + x * log(1 - x^4/24)).
Original entry on oeis.org
1, 0, 0, 0, 0, 5, 0, 0, 0, 315, 6300, 0, 0, 150150, 6306300, 94594500, 0, 268017750, 17689171500, 549972423000, 7332965640000, 1283268987000, 117632990475000, 5681673439942500, 155840185781280000, 1961530116170625000, 1606200062942475000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^4/24))))
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a(n) = n!*sum(k=0, n\4, (n-4*k)!*abs(stirling(k, n-4*k, 1))/(24^k*k!));
A375586
Expansion of e.g.f. 1 / (1 + x - x * exp(x^2/2)).
Original entry on oeis.org
1, 0, 0, 3, 0, 15, 180, 105, 5040, 46305, 132300, 3752595, 33679800, 243378135, 5565940380, 56191160025, 712410098400, 14889814164225, 183558878603100, 3236148386145675, 66650136566013000, 1027807726886515575, 21983938825036488300, 469896981350215644225
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2/2))))
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a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(k, n-2*k, 2)/(2^k*k!));
A375682
Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^3.
Original entry on oeis.org
1, 0, 0, 9, 0, 45, 1080, 630, 30240, 470610, 1247400, 38170440, 523908000, 3454050600, 87950182320, 1245647403000, 14580569203200, 346019491818000, 5524280291930400, 92520760776444000, 2188180621979352000, 40781057935225608000, 857154570994798876800
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2/2))^3))
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a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*abs(stirling(k, n-2*k, 1))/(2^k*k!))/2;
Showing 1-5 of 5 results.