A162632
G.f. is the polynomial (Product_{k=1..14} (1 - x^(3*k)))/(1-x)^14.
Original entry on oeis.org
1, 14, 105, 559, 2366, 8463, 26571, 75126, 194817, 469728, 1064166, 2284086, 4675748, 9179014, 17358666, 31744441, 56319263, 97205511, 163611175, 269111465, 433356858, 684315658, 1061177819, 1618066905, 2428728445
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..14]])/(1-x)^14; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=14: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..24); # Muniru A Asiru, Jul 07 2018
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CoefficientList[Series[(Times@@(1-x^(3*Range[14])))/(1-x)^14,{x,0,30}],x] (* Harvey P. Dale, Apr 28 2018 *)
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x='x+O('x^50); A = prod(k=1, 14, (1-x^(3*k)))/(1-x)^14; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162635
G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) * (1-x^30) * (1-x^33) * (1-x^36) * (1-x^39) * (1-x^42) * (1-x^45) / (1-x)^15.
Original entry on oeis.org
1, 15, 120, 679, 3045, 11508, 38079, 113205, 308022, 777750, 1841916, 4126002, 8801750, 17980764, 35339430, 67083871, 123403134, 220608645, 384219820, 653331285, 1086688143, 1771003801, 2832181620, 4450248525, 6878976970
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..15]])/(1-x)^15; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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P:= normal((1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) * (1-x^30) * (1-x^33) * (1-x^36) * (1-x^39) * (1-x^42) * (1-x^45) / (1-x)^15):
seq(coeff(P,x,n),n=0..degree(P)); # Robert Israel, Jul 06 2018
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CoefficientList[Series[Times@@(1-x^(3*Range[15]))/(1-x)^15, {x, 0, 50}], x] (* G. C. Greubel, Jul 06 2018 *)
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x='x+O('x^50); A = prod(k=1, 15, (1-x^(3*k)))/(1-x)^15; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162636
G.f. is the polynomial (Product_{k=1..16} (1 - x^(3*k)))/(1-x)^16.
Original entry on oeis.org
1, 16, 136, 815, 3860, 15368, 53447, 166652, 474674, 1252424, 3094340, 7220342, 16022092, 34002856, 69342286, 136426157, 259829291, 480437936, 864657756, 1517989041, 2604677184, 4375680985, 7207862605, 11658111130, 18537088100
Offset: 0
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m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..16]])/(1-x)^16; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=16: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..24); # Muniru A Asiru, Jul 07 2018
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CoefficientList[Series[(Times@@Table[(1-x^(3n)),{n,16}])/(1-x)^16,{x,0,40}],x] (* Harvey P. Dale, Jul 23 2013 *)
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x='x+O('x^50); A = prod(k=1, 16, (1-x^(3*k)))/(1-x)^16; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162637
G.f. is the polynomial (Product_{k=1..17} (1 - x^(3*k)))/(1-x)^17.
Original entry on oeis.org
1, 17, 153, 968, 4828, 20196, 73643, 240295, 714969, 1967393, 5061733, 12282075, 28304167, 62307023, 131649309, 268075466, 527904757, 1008342693, 1873000449, 3390989490, 5995666674, 10371347659, 17579210264, 29237321394, 47774409494
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..17]])/(1-x)^17; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=17: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..24); # Muniru A Asiru, Jul 07 2018
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CoefficientList[Series[Times@@(1-x^(3*Range[17]))/(1-x)^17, {x, 0, 50}], x] (* G. C. Greubel, Jul 06 2018 *)
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x='x+O('x^50); A = prod(k=1, 17, (1-x^(3*k)))/(1-x)^17; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162638
G.f. is the polynomial (Product_{k=1..18} (1 - x^(3*k)))/(1-x)^18.
Original entry on oeis.org
1, 18, 171, 1139, 5967, 26163, 99806, 340101, 1055070, 3022463, 8084196, 20366271, 48670438, 110977461, 242626770, 510702236, 1038606993, 2046949686, 3919950135, 7310939625, 13306606299, 23677953958, 41257164222, 70494485616
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..18]])/(1-x)^18; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=18: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..23); # Muniru A Asiru, Jul 07 2018
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CoefficientList[Series[Times@@(1-x^(3*Range[18]))/(1-x)^18, {x, 0, 50}], x] (* G. C. Greubel, Jul 06 2018 *)
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x='x+O('x^50); A = prod(k=1, 18, (1-x^(3*k)))/(1-x)^18; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162639
G.f. is the polynomial (Product_{k=1..19} (1 - x^(3*k)))/(1-x)^19.
Original entry on oeis.org
1, 19, 190, 1329, 7296, 33459, 133265, 473366, 1528436, 4550899, 12635095, 33001366, 81671804, 192649265, 435276035, 945978271, 1984585264, 4031534950, 7951485085, 15262424710, 28569031009, 52246984967, 93504149189
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..19]])/(1-x)^19; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=19: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..22); # Muniru A Asiru, Jul 07 2018
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CoefficientList[Series[Times@@(1-x^Range[3,57,3])/(1-x)^19,{x,0,30}],x] (* Harvey P. Dale, Apr 30 2018 *)
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x='x+O('x^50); A = prod(k=1, 19, (1-x^(3*k)))/(1-x)^19; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162640
G.f. is the polynomial (Product_{k=1..20} (1 - x^(3*k)))/(1-x)^20.
Original entry on oeis.org
1, 20, 210, 1539, 8835, 42294, 175559, 648925, 2177361, 6728260, 19363355, 52364721, 134036525, 326685790, 761961825, 1707940096, 3692525360, 7724060310, 15675545395, 30937970105, 59507001114, 111753986081
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..20]])/(1-x)^20; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=20: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..21); # Muniru A Asiru, Jul 07 2018
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CoefficientList[Series[Times@@Table[1-x^n,{n,3,60,3}]/(1-x)^20, {x,0,30}],x] (* Harvey P. Dale, May 06 2012 *)
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x='x+O('x^50); A = prod(k=1, 20, (1-x^(3*k)))/(1-x)^20; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162646
G.f. is the polynomial (Product_{k=1..21} (1 - x^(3*k)))/(1-x)^21.
Original entry on oeis.org
1, 21, 231, 1770, 10605, 52899, 228458, 877383, 3054744, 9783004, 29146359, 81511080, 215547605, 542233395, 1304195220, 3012135316, 6704660676, 14428720986, 30104266381, 61042236486, 120549237600, 232303223681
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..21]])/(1-x)^21; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=21: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..21); # Muniru A Asiru, Jul 07 2018
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CoefficientList[Series[Times@@(1-x^(3*Range[21]))/(1-x)^21, {x, 0, 50}], x] (* G. C. Greubel, Jul 06 2018 *)
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x='x+O('x^50); A = prod(k=1, 21, (1-x^(3*k)))/(1-x)^21; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162679
G.f. is the polynomial (Product_{k=1..22} (1 - x^(3*k)))/(1-x)^22.
Original entry on oeis.org
1, 22, 253, 2023, 12628, 65527, 293985, 1171368, 4226112, 14009116, 43155475, 124666555, 340214160, 882447555, 2186642775, 5198778091, 11903438767, 26332159753, 56436426134, 117478662620, 238027900220, 470331123901
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..22]])/(1-x)^22; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=22: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..21); # Muniru A Asiru, Jul 07 2018
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With[{num=Times@@(1-x^Range[3,66,3])},CoefficientList[Series[num/(1-x)^22,{x,0,40}],x]] (* Harvey P. Dale, Dec 31 2012 *)
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x='x+O('x^50); A = prod(k=1, 22, (1-x^(3*k)))/(1-x)^22; Vec(A) \\ G. C. Greubel, Jul 06 2018
A162680
G.f. is the polynomial (Product_{k=1..23} (1 - x^(3*k)))/(1-x)^23.
Original entry on oeis.org
1, 23, 276, 2299, 14927, 80454, 374439, 1545807, 5771919, 19781035, 62936510, 187603065, 527817225, 1410264780, 3596907555, 8795685646, 20699124413, 47031284166, 103467710300, 220946372920, 458974273140, 929305397041
Offset: 0
-
m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..23]])/(1-x)^23; Coefficients(R!(F)); // G. C. Greubel, Jul 06 2018
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m:=23: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..21); # Muniru A Asiru, Jul 07 2018
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CoefficientList[Series[Times@@(1-x^(3*Range[23]))/(1-x)^23,{x,0,30}],x] (* Harvey P. Dale, Jun 04 2017 *)
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x='x+O('x^50); A = prod(k=1, 23, (1-x^(3*k)))/(1-x)^23; Vec(A) \\ G. C. Greubel, Jul 06 2018
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