A143760
a(n+1) = a(n)^2 + n^2, a(1) = 1.
Original entry on oeis.org
1, 2, 8, 73, 5345, 28569050, 816190617902536, 666167124752123519223995231345, 443778638100511299954105018279514127887014869775300070509089
Offset: 1
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RecurrenceTable[{a[1]==1,a[n]==a[n-1]^2+(n-1)^2},a[n],{n,10}] (* Harvey P. Dale, May 03 2011 *)
A143761
a(n+1) = a(n)^2 - n*a(n) + n^2, a(1) = 1.
Original entry on oeis.org
1, 1, 3, 9, 61, 3441, 11819871, 139709267717593, 19518679486184955909459972969, 380978848884417414427615903969045678210740619589070918321
Offset: 1
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RecurrenceTable[{a[n+1] == a[n]^2 - n*a[n] + n^2, a[1] == 1}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
nxt[{n_,a_}]:={n+1,a^2-a(n+1)+(n+1)^2}; Join[{1},NestList[nxt,{1,1},10][[All,2]]] (* Harvey P. Dale, Oct 15 2017 *)
A143762
a(n+1) = a(n)^2 + n*a(n) + n^2, a(1) = 1.
Original entry on oeis.org
1, 3, 19, 427, 184053, 33876427099, 1147612313197120118431, 1317014021401644919149757309088631306730827, 1734525932568532421128602190712731410907662021613907396581559184320372648524685950609
Offset: 1
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RecurrenceTable[{a[n+1] == a[n]^2 + n*a[n] + n^2, a[1] == 1}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
nxt[{n_, a_}] := {n + 1, a^2 + n*a + n^2}; NestList[nxt,{1,1},10][[All,2]] (* Harvey P. Dale, Sep 12 2018 *)
A143763
a(n+1) = (a(n)-n)^2, a(1) = 1.
Original entry on oeis.org
1, 0, 4, 1, 9, 16, 100, 8649, 74666881, 5575141774264384, 31082205803147712138788845611876, 966103517589229313003894215813508352493573272034098666228778225
Offset: 1
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a=1;Table[a=(n-a)^2,{n,0,16}] (* Vladimir Joseph Stephan Orlovsky, Nov 20 2009 *)
RecurrenceTable[{a[n+1] == (a[n]-n)^2, a[1] == 1}, a, {n, 1, 15}] (* Vaclav Kotesovec, Dec 18 2014 *)
nxt[{n_,a_}]:={n+1,(a-n)^2}; NestList[nxt,{1,1},12][[All,2]] (* Harvey P. Dale, Feb 02 2022 *)
A143765
a(n+1) = a(n)^2 - 3*n*a(n) + n^2, a(1) = 1.
Original entry on oeis.org
1, -1, 11, 31, 605, 356975, 127424725111, 16237060566937994735039, 263642135854412795003324875413502371940690649, 69507175797876652622009028770643203522181284529919017784559264153993383198392412717393759
Offset: 1
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RecurrenceTable[{a[n+1] == a[n]^2 - 3*n*a[n] + n^2, a[1] == 1}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
A143766
a(n+1) = a(n)^2 + 3*n*a(n) + n^2, a(1) = 1.
Original entry on oeis.org
1, 5, 59, 4021, 16216709, 262981894041341, 69159476593575838635509822455, 4783033202697364284917104840982811414253511628131328498629, 22877406618105405861781317490149379589769149890660405723416585348109182559037843469373513563751798569651299138846801
Offset: 1
Contribution from _Reinhard Zumkeller_, Sep 11 2008: (Start)
a(4)=A000040(556);
a(5)=19*199*4289;
a(6)=3686299*71340359;
a(7)=5*89*23581*36190079671*182112572569;
A055642(a(8))=58; A001221(a(8))=A001222(a(8))=3;
A055642(A020639(a(8)))=4, A020639(a(8))=2459;
A055642(A006530(a(8)))=43, A006530(a(8))=1145781805709434583439407716589323093429591;
A055642(a(9))=116; A001221(a(9))=A001222(a(9))=3;
A055642(A020639(a(9)))=5, A020639(a(9))=52291;
A055642(A087039(a(9)))=39, A087039(a(9))=823717865733493312451872329574156137131;
A055642(A006530(a(9)))=72, A006530(a(9))=531130643259166452223939782963931943654770628199012648274446497807560081;
factorizations made with Dario Alpern's ECM applet. (End)
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RecurrenceTable[{a[n+1] == a[n]^2 + 3*n*a[n] + n^2, a[1] == 1}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
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