A375172
Expansion of e.g.f. exp( x^2/(1-x)^3 ) / (1-x).
Original entry on oeis.org
1, 1, 4, 30, 276, 2940, 36120, 507360, 8032080, 141235920, 2725107840, 57151211040, 1293129351360, 31376876731200, 812303844992640, 22338850742208000, 650081402588217600, 19951131574037664000, 643805564147435289600, 21785365857810973017600
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/(1-x)^3)/(1-x)))
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a(n) = n!*sum(k=0, n\2, binomial(n+k, n-2*k)/k!);
A361594
Expansion of e.g.f. exp( (x / (1-x))^2 ) / (1-x).
Original entry on oeis.org
1, 1, 4, 24, 180, 1620, 17040, 204960, 2770320, 41504400, 681791040, 12173293440, 234555773760, 4847900016960, 106932303878400, 2506094618227200, 62165827044921600, 1626693694039814400, 44767280999939097600, 1292282276155782912000
Offset: 0
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Table[n! * Sum[Binomial[n,2*k]/k!, {k,0,n/2}], {n,0,20}] (* Vaclav Kotesovec, Mar 17 2023 *)
With[{nn=20},CoefficientList[Series[Exp[(x/(1-x))^2]/(1-x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 29 2023 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^2)/(1-x)))
A375226
Expansion of e.g.f. exp( (x / (1-x))^3 ) / (1-x)^2.
Original entry on oeis.org
1, 2, 6, 30, 240, 2520, 30600, 413280, 6168960, 101666880, 1842825600, 36483955200, 782548905600, 18048500870400, 444816333561600, 11656620213638400, 323500679915212800, 9475966585948262400, 292101319958063616000, 9450373008137757696000
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^3)/(1-x)^2))
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a(n) = n!*sum(k=0, n\3, binomial(n+1, n-3*k)/k!);
A375227
Expansion of e.g.f. exp( (x / (1-x))^3 ) / (1-x)^3.
Original entry on oeis.org
1, 3, 12, 66, 504, 5040, 60840, 839160, 12882240, 217607040, 4018896000, 80691811200, 1750850640000, 40809559190400, 1016150162227200, 26898872647046400, 753882642267955200, 22291971504503500800, 693356807039126630400
Offset: 0
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With[{nn=20},CoefficientList[Series[Exp[(x/(1-x))^3]/(1-x)^3,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 04 2025 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^3)/(1-x)^3))
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a(n) = n!*sum(k=0, n\3, binomial(n+2, n-3*k)/k!);
Showing 1-4 of 4 results.