A375409
Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x).
Original entry on oeis.org
1, 0, 3, 2, 33, 84, 835, 4542, 42273, 353672, 3670371, 39704730, 480066433, 6221189532, 87210179043, 1307488285334, 20923882733505, 355680675491472, 6402415875542083, 121644826003391922, 2432903816934178401, 51090929833475100260, 1124000813126981130243
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x))/(1-x)))
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a(n) = (-1)^n*n!*sum(k=0, n, binomial(k-1, n-k)/k!);
A375411
Expansion of e.g.f. exp(-x * (1 - x)^3) / (1 - x).
Original entry on oeis.org
1, 0, 7, -16, 177, -1096, 10975, -94872, 1101121, -11699632, 151701111, -1897734400, 27287272177, -385421578296, 6100570870927, -95315920570696, 1642003509857025, -27968228816277472, 520462884927746791, -9551232423922438512, 190797743531054785201
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^3)/(1-x)))
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a(n) = (-1)^n*n!*sum(k=0, n, binomial(3*k-1, n-k)/k!);
A375413
Expansion of e.g.f. exp(x^2 * (1 - x)^2) / (1 - x).
Original entry on oeis.org
1, 1, 4, 0, 36, -60, 1920, -1680, 109200, -347760, 9858240, -27941760, 1321911360, -3675672000, 210819248640, -422918496000, 45482678841600, 432259027200, 11915705273472000, 32436011672064000, 3902063601673036800, 25891695005316940800, 1575143884245502771200
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2*(1-x)^2)/(1-x)))
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a(n) = (-1)^n*n!*sum(k=0, n\2, binomial(2*k-1, n-2*k)/k!);
A375415
Expansion of e.g.f. exp(-x^3 * (1 - x)^2) / (1 - x).
Original entry on oeis.org
1, 1, 2, 0, 48, 120, 1080, -2520, 100800, 120960, 6652800, -26611200, 1297296000, -778377600, 177989011200, -610248038400, 53004401049600, -62245299916800, 12760286482944000, -13009267682611200, 5173295797942272000, 3608804645462016000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^3*(1-x)^2)/(1-x)))
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a(n) = (-1)^n*n!*sum(k=0, n\3, binomial(2*k-1, n-3*k)/k!);
A375426
Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x)^2.
Original entry on oeis.org
1, 1, 7, 17, 149, 569, 6019, 34033, 409513, 3261041, 42986591, 451422641, 6486586237, 84605091817, 1334440837339, 20632779265169, 358963187353169, 6363955245003233, 122111809463225143, 2427035466387882961, 51167058284040281701, 1122982719058921672601
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)^2))
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a(n) = (-1)^n*n!*sum(k=0, n, binomial(2*k-2, n-k)/k!);
A375427
Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x)^3.
Original entry on oeis.org
1, 2, 11, 50, 349, 2314, 19903, 173354, 1796345, 19428146, 237268051, 3061371202, 43223040661, 646504620410, 10385505523079, 176415362111354, 3181608981134833, 60451307924295394, 1210235352100542235, 25421507156298185426, 559597201410003990221
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)^3))
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a(n) = (-1)^n*n!*sum(k=0, n, binomial(2*k-3, n-k)/k!);
Showing 1-6 of 6 results.