A375410
Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x).
Original entry on oeis.org
1, 0, 5, -4, 81, -176, 2605, -8100, 137249, -424576, 10376181, -21429860, 1069514545, 279470736, 149969551901, 616166705084, 28838719110465, 261581059999360, 7560615053166949, 106911086586605244, 2626348956282622481, 48474495094075756880, 1160413567193463596685
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)))
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a(n) = (-1)^n*n!*sum(k=0, n, binomial(2*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!);
A375412
Expansion of e.g.f. exp(x^2 * (1 - x)) / (1 - x).
Original entry on oeis.org
1, 1, 4, 6, 36, 60, 840, 3360, 48720, 317520, 4112640, 36923040, 503616960, 5976210240, 89132883840, 1287955468800, 21130876166400, 353720208441600, 6424780602240000, 121392008337600000, 2435685015296332800, 51056321187692620800, 1124423866880349235200
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2*(1-x))/(1-x)))
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a(n) = (-1)^n*n!*sum(k=0, n\2, binomial(k-1, n-2*k)/k!);
A375414
Expansion of e.g.f. exp(-x^3 * (1 - x)) / (1 - x).
Original entry on oeis.org
1, 1, 2, 0, 24, 120, 1080, 2520, 40320, 302400, 4838400, 33264000, 498960000, 5448643200, 98075577600, 1242290649600, 21620216217600, 337903056691200, 6624678348288000, 119786633597030400, 2466692313845760000, 50371208660957184000, 1133144384491671552000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^3*(1-x))/(1-x)))
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a(n) = (-1)^n*n!*sum(k=0, n\3, binomial(k-1, n-3*k)/k!);
A375424
Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x)^2.
Original entry on oeis.org
1, 1, 5, 17, 101, 589, 4369, 35125, 323273, 3263129, 36301661, 439023001, 5748342445, 80949641317, 1220505157481, 19615065647549, 334764933094289, 6046684538094385, 115242737561241013, 2311256839666971169, 48658040610273601781, 1072909782649220737661
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x))/(1-x)^2))
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a(n) = (-1)^n*n!*sum(k=0, n, binomial(k-2, n-k)/k!);
A375425
Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x)^3.
Original entry on oeis.org
1, 2, 9, 44, 277, 1974, 16213, 148616, 1512201, 16872938, 205031041, 2694364452, 38080715869, 575998947614, 9284490424077, 158882422008704, 2876883685233553, 54953707187064786, 1104409466928407161, 23295036711306707228, 514558774836407746341
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x))/(1-x)^3))
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a(n) = (-1)^n*n!*sum(k=0, n, binomial(k-3, n-k)/k!);
Showing 1-6 of 6 results.