A366298
Expansion of e.g.f. 1 / (-2 + Sum_{k=1..3} exp(-k*x)).
Original entry on oeis.org
1, 6, 58, 828, 15766, 375276, 10719118, 357202068, 13603819126, 582854637276, 27747071520478, 1453003753611108, 83005119616449286, 5136947527401250476, 342365553703113120238, 24447711909762202272948, 1862151878019906517540246, 150702660087903415402794876, 12913688931657425188926182398
Offset: 0
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nmax = 18; CoefficientList[Series[1/(-2 + Sum[Exp[-k x], {k, 1, 3}]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k] (1 + 2^k + 3^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
A366299
Expansion of e.g.f. 1 / (-3 + Sum_{k=1..4} exp(-k*x)).
Original entry on oeis.org
1, 10, 170, 4300, 145046, 6115900, 309453710, 18267444100, 1232400398966, 93535914320620, 7887919177776350, 731710341934820500, 74046493229735962886, 8117679564133907097340, 958393800813241073719790, 121232569802975799394430500, 16357741845227058108680934806, 2345072789674603792983906178060
Offset: 0
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nmax = 17; CoefficientList[Series[1/(-3 + Sum[Exp[-k x], {k, 1, 4}]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k] (1 + 2^k + 3^k + 4^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]
A366300
Expansion of e.g.f. 1 / (-4 + Sum_{k=1..5} exp(-k*x)).
Original entry on oeis.org
1, 15, 395, 15525, 813671, 53306325, 4190730335, 384368222925, 40289992211591, 4751157347330085, 622528350091484975, 89724601853904952125, 14107579506569655343511, 2403010007367884873188245, 440801776092151383251034815, 86635186648455606881413582125, 18162432724968339044562784395431
Offset: 0
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nmax = 16; CoefficientList[Series[1/(-4 + Sum[Exp[-k x], {k, 1, 5}]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k] (1 + 2^k + 3^k + 4^k + 5^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]
A366301
Expansion of e.g.f. 1 / (-5 + Sum_{k=1..6} exp(-k*x)).
Original entry on oeis.org
1, 21, 791, 44541, 3344327, 313883661, 35351663831, 4645129190541, 697553757742247, 117844709608925901, 22120757207544654071, 4567542244067740041741, 1028853921587420129556167, 251065459281889114259025741, 65978874409961267115296383511, 18577448234544937135538443584141
Offset: 0
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nmax = 15; CoefficientList[Series[1/(-5 + Sum[Exp[-k x], {k, 1, 6}]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k] (1 + 2^k + 3^k + 4^k + 5^k + 6^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]
Showing 1-4 of 4 results.