A144690
Limit of the coefficient of x^(2^m+n) in B(x)^(n+1) as m grows, where B(x) = Sum_{k>=0} x^(2^k).
Original entry on oeis.org
1, 2, 6, 16, 130, 636, 5712, 34336, 811458, 7151380, 113034746, 1049982792, 25276020640, 293841338896, 5712436923000, 68827002466176, 3739997267623490, 60752008945662372, 1718332635327516238, 26832922324005759560, 1099199814287516279394
Offset: 0
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{ a(n) = local(m=n+log(n+.5)\log(2), B=sum(k=0,m,x^(2^k)));if(n<0, 0, polcoeff((B+O(x^(2^m+n+1)))^(n+1),2^m+n)) }
a(14), a(15) corrected and a(16)-a(23) added by
Max Alekseyev, May 03 2011
A135068
a(n) = [x^(2^n+n-1)] (x + x^2 + x^4 + x^8 + ... + x^2^n)^n for n>=1.
Original entry on oeis.org
1, 2, 6, 16, 90, 636, 5712, 34336, 537282, 5941780, 99729146, 1049982792, 23200347040, 293841338896, 5712436923000, 68827002466176, 2844850573581890, 53069160498788772, 1545326270301621838, 26021954987946879560, 1020860369624228471394, 19905401189634441143740, 605270985059438427438138, 11141784565490367848976336, 621465511993167908247508400, 14470690420043042111787089216, 548187222712632324159956010732, 11881058908943228840652007583056
Offset: 1
-
f[x_, n_] := (Sum[x^(2^k), {k, 0, n}])^n; Table[Coefficient[f[x, n], x^(2^n + n - 1)] , {n, 1, 20}] (* G. C. Greubel, Sep 22 2016 *)
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a(n)=if(n<1,0,polcoeff(sum(j=0,n,x^(2^j)+O(x^(2^n+n)))^n,2^n+n-1))
A135069
a(n) = [x^(2^n+n-1)] (x + x^2 + x^4 + x^8 + ... + x^(2^n))^n / n for n>=1.
Original entry on oeis.org
1, 1, 2, 4, 18, 106, 816, 4292, 59698, 594178, 9066286, 87498566, 1784642080, 20988667064, 380829128200, 4301687654136, 167344151387170, 2948286694377154, 81332961594822202, 1301097749397343978, 48612398553534689114, 904790963165201870170, 26316129785192975106006, 464241023562098660374014, 24858620479726716329900336, 556565016155501619684118816, 20303230470838234228146518916, 424323532462258172880428842252
Offset: 1
-
f[x_, n_] := (1/n)*(Sum[x^(2^k), {k, 0, n}])^n; Table[Coefficient[f[x, n], x^(2^n + n - 1)] , {n, 1, 10}] (* G. C. Greubel, Sep 22 2016 *)
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{a(n)=if(n<1,0,polcoeff(sum(j=0,n,x^(2^j)+O(x^(2^n+n)))^n,2^n+n-1)/n)}
A135070
a(n) = [x^(2^n+n-2)] (x + x^2 + x^4 + x^8 + ... + x^(2^n))^n for n>=1.
Original entry on oeis.org
1, 1, 3, 18, 70, 600, 4956, 52528, 358128, 6654600, 79967800, 1453049400, 16239408120, 392541718660, 5252687631660, 108961629396480, 1395025456201408, 62831427044385384, 1223872353413404344, 37391632408971430120, 655014723078024641640, 27055523795138159291124, 547691411941958414420092, 17365164578604322437671664, 332211955074827711097949200, 19385342415197943809053622700, 466687147661484232610990714436, 18326221432646410203582181439808
Offset: 1
-
f[x_, n_] := (Sum[x^(2^k), {k, 0, n}])^n; Table[Coefficient[f[x, n], x^(2^n + n - 2)] , {n, 2, 10}] (* G. C. Greubel, Sep 22 2016 *)
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{a(n)=if(n<2,0,polcoeff(sum(j=0,n,x^(2^j)+O(x^(2^n+n)))^n,2^n+n-2))}
a(1) prepended and a(20)-a(28) added by
Max Alekseyev, Aug 31 2024
Showing 1-4 of 4 results.
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