A294188
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(k*(1/(1-x)^k - 1)).
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 4, 3, 0, 1, 9, 28, 13, 0, 1, 16, 117, 256, 73, 0, 1, 25, 336, 1881, 2848, 501, 0, 1, 36, 775, 8416, 35505, 37024, 4051, 0, 1, 49, 1548, 27925, 241696, 763209, 547936, 37633, 0, 1, 64, 2793, 75888, 1134025, 7769856, 18309861, 9064192
Offset: 0
Square array A(n,k) begins:
1, 1, 1, 1, 1, ...
0, 1, 4, 9, 16, ...
0, 3, 28, 117, 336, ...
0, 13, 256, 1881, 8416, ...
0, 73, 2848, 35505, 241696, ...
0, 501, 37024, 763209, 7769856, ...
A294047
a(n) = n! * [x^n] exp(1/(1-x)^n - 1).
Original entry on oeis.org
1, 1, 10, 195, 6136, 280745, 17452296, 1406162695, 141881576320, 17464107109329, 2568781033444000, 444027365181074411, 88960718926056936960, 20419945656807380230105, 5317219394033953475875456, 1557341699638685065316319375, 509241278697083918035944964096
Offset: 0
-
S:=series(exp(1/(1-x)^n-1),x,31):
seq(n!*coeff(S,x,n),n=0..30); # Robert Israel, Oct 22 2017
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Table[n!*SeriesCoefficient[Exp[1/(1-x)^n - 1], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 22 2017 *)
A294050
E.g.f.: exp(1/(1-x)^4 - 1).
Original entry on oeis.org
1, 4, 36, 424, 6136, 104544, 2037856, 44549824, 1076383296, 28423224064, 813041441536, 25012265117184, 822613038178816, 28777151476086784, 1066188308742567936, 41680239704335888384, 1713629127784250085376, 73882449584935612268544
Offset: 0
-
nmax = 20; CoefficientList[Series[Exp[1/(1-x)^4 - 1], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 22 2017 *)
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N=66; x='x+O('x^N); Vec(serlaplace(exp(1/(1-x)^4-1)))
A294051
Expansion of e.g.f.: exp(1/(1-x)^5 - 1).
Original entry on oeis.org
1, 5, 55, 785, 13705, 280745, 6561175, 171559925, 4947814225, 155676898925, 5297647127575, 193609855201625, 7554669411801625, 313185598385812625, 13735697420477200375, 634998741428031792125, 30844527567399706110625, 1569784302914751616023125
Offset: 0
-
nmax = 20; CoefficientList[Series[Exp[1/(1-x)^5 - 1], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 22 2017 *)
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N=66; x='x+O('x^N); Vec(serlaplace(exp(1/(1-x)^5-1)))
Showing 1-4 of 4 results.