A143635
E.g.f. satisfies: A(x) = exp(x*A(((x+1)^4-1)/4)).
Original entry on oeis.org
1, 1, 3, 25, 329, 6471, 175747, 6222259, 277683681, 15206462497, 1000136567591, 77666331244239, 7021789807671817, 730394622232111747, 86529393614846902371, 11573498785704862459891, 1734360074041552070631713
Offset: 0
-
A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,4)(x), x,n)*n!: seq(a(n), n=0..21);
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A[n_, k_] := A[n, k] = Module[{f}, f = Function[If[n <= 0 || k == 0, 1, A[n-1, k][((#+1)^k-1)/k]]]; Function[Normal[Series[Exp[x*f[x]], {x, 0, n+1}]] /. x -> #]]; a[n_] := SeriesCoefficient[A[n, 4][x], {x, 0, n}]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 13 2014, after Maple *)
A143633
E.g.f. satisfies: A(x) = exp(x*A(((x+1)^2-1)/2)).
Original entry on oeis.org
1, 1, 3, 19, 185, 2541, 45787, 1037359, 28649553, 942585625, 36294146171, 1612599520599, 81729515092777, 4679679856932133, 300257015404355115, 21436580394615666991, 1692530428442960006753, 146987828523665177048241
Offset: 0
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A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp (x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,2)(x), x,n)*n!: seq(a(n), n=0..21);
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A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 2][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)
A143634
E.g.f. satisfies: A(x) = exp(x*A(((x+1)^3-1)/3)).
Original entry on oeis.org
1, 1, 3, 22, 253, 4256, 96727, 2828274, 102988937, 4553158024, 239618067211, 14775790894734, 1053758625896077, 85965003368491300, 7947211237328151167, 825821792546485330306, 95772123012223308982673
Offset: 0
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A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,3)(x), x,n)*n!: seq(a(n), n=0..21);
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A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 3][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)
A143636
E.g.f. satisfies: A(x) = exp(x*A(((x+1)^5-1)/5)).
Original entry on oeis.org
1, 1, 3, 28, 413, 9216, 289111, 11925964, 624637785, 40422282112, 3159287760491, 292875271947468, 31733363437993285, 3969285168539789008, 567118401777735330447, 91714059231986721233596
Offset: 0
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A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,5)(x), x,n)*n!: seq(a(n), n=0..21);
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A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 5][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)
A143637
E.g.f. satisfies: A(x) = exp(x*A(((x+1)^6-1)/6)).
Original entry on oeis.org
1, 1, 3, 31, 505, 12521, 443227, 20766159, 1240975409, 92068494625, 8282460205891, 886498379552919, 111190541933344777, 16136424098890466281, 2680205744964849259355, 504746978220729054647911, 106901213223866930807470433, 25280598116469824339521406081
Offset: 0
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A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,6)(x), x,n)*n!: seq(a(n), n=0..20);
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A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 6][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)
A143638
E.g.f. satisfies: A(x) = exp(x*A(((x+1)^7-1)/7)).
Original entry on oeis.org
1, 1, 3, 34, 605, 16416, 644647, 33690574, 2252245353, 187575203080, 19000833293771, 2295318297423834, 325536649109809117, 53508774130762119508, 10080999100649218887615, 2156137639664134179951166, 519200838601168582073365073, 139740129055162031424178122096
Offset: 0
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A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,7)(x), x,n)*n!: seq(a(n), n=0..20);
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A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 7][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)
A143639
E.g.f. satisfies: A(x) = exp(x*A(((x+1)^8-1)/8)).
Original entry on oeis.org
1, 1, 3, 37, 713, 20931, 900067, 51768739, 3815631297, 351259985449, 39429531406511, 5287999813256799, 833815716731955817, 152569133029591977895, 32033950906843181020467, 7643291957710224206903131, 2055010408602517321146955553, 618032357523179035120686532401
Offset: 0
-
A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,8)(x), x,n)*n!: seq(a(n), n=0..20);
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A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 8][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)
A143640
E.g.f. satisfies: A(x) = exp(x*A(((x+1)^9-1)/9)).
Original entry on oeis.org
1, 1, 3, 40, 829, 26096, 1216327, 76192824, 6123167801, 615764308672, 75666884850091, 11126407433017944, 1925795142055097557, 387184416676122044032, 89407267196505737775311, 23480531627128442036603416, 6953687155109949099972629873
Offset: 0
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A:= proc(n,k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1,k)(((x+1)^k-1)/k) fi; unapply(convert(series(exp(x*%), x,n+1), polynom), x) end: a:= n-> coeff(A(n,9)(x), x,n)*n!: seq(a(n), n=0..20);
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A[n_, k_] := Module[{f}, f[x_] = If[n <= 0 || k == 0, 1, A[n-1, k][((x+1)^k-1)/k]]; Normal[Series[Exp[x*f[x]], { x, 0, n+1}]] /. x -> #]&; a[n_] := Coefficient[A[n, 9][x], x, n]*n!; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Feb 14 2014, after Maple *)
A306578
a(n) = n! * [x^n] A_n(x) with A_n(x) = exp(x*A_n(((x+1)^n-1)/n)) if n > 0 and A_0(x) = exp(x).
Original entry on oeis.org
1, 1, 3, 22, 329, 9216, 443227, 33690574, 3815631297, 615764308672, 136379590946891, 40153740607226214, 15306924742075555657, 7392759013812560317840, 4441824191762733091989051, 3268365147290283563408293846, 2905065653907985007147484366113
Offset: 0
Showing 1-9 of 9 results.