cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-15 of 15 results.

A000393 Number of n-node rooted trees of height 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 6, 26, 94, 308, 941, 2744, 7722, 21166, 56809, 149971, 390517, 1005491, 2564164, 6485901, 16289602, 40659669, 100934017, 249343899, 613286048, 1502515487, 3667953650, 8925161513, 21652815724, 52387028291
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Column h=6 of A034781.

Programs

  • Maple
    For Maple program see link in A000235.
  • Mathematica
    f[n_] := Nest[CoefficientList[Series[Product[1/(1 - x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x] &, {1}, n];f[6]-f[5] (* Geoffrey Critzer, Aug 01 2013 *)

Formula

A034823-A001385. - Christian G. Bower

A000418 Number of n-node rooted trees of height 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 7, 34, 136, 487, 1615, 5079, 15349, 45009, 128899, 362266, 1002681, 2740448, 7411408, 19865445, 52840977, 139624510, 366803313, 958696860, 2494322662, 6463281890, 16686206047, 42935345688, 110142163940, 281763465941
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Column h=7 of A034781.

Programs

  • Maple
    For Maple program see link in A000235.
  • Mathematica
    b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1 || k < 1, 0, Sum[ Binomial[b[i - 1, i - 1, k - 1] + j - 1, j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]]; a[n_] := b[n - 1, n - 1, 7] - b[n - 1, n - 1, 6]; Array[a, 40] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A034781 *)

Formula

A034824-A034823. - Christian G. Bower

A000429 Number of n-node rooted trees of height 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 43, 188, 728, 2593, 8706, 27961, 86802, 262348, 776126, 2256418, 6466614, 18311915, 51334232, 142673720, 393611872, 1078955836, 2941029334, 7977065816, 21541492856, 57942770689, 155304829763, 414934057486
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Column h=8 of A034781.

Programs

  • Maple
    For Maple program see link in A000235.
  • Mathematica
    b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1 || k < 1, 0, Sum[ Binomial[b[i - 1, i - 1, k - 1] + j - 1, j]*b[n - i*j, i - 1, k], {j, 0, n/i}]]]; a[n_] := b[n - 1, n - 1, 8] - b[n - 1, n - 1, 7]; Array[a, 40] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A034781 *)

Formula

a(n) = A034825(n) - A034824(n). - Christian G. Bower

A034826 Number of n-node rooted trees of height at most 9.

Original entry on oeis.org

1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1841, 4755, 12410, 32558, 85849, 226980, 601373, 1594870, 4232100, 11230771, 29798539, 79034638, 209526631, 555172356, 1470195001, 3891131705, 10292857772, 27212082536, 71905725130, 189911518888
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

See A001383 for details.

Programs

  • Maple
    For Maple program see link in A000235.
with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d,j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: shr:= proc(p) n->`if`(n=0, 1,p(n-1)) end: b[0]:= etr(n->1): for j from 1 to 7 do b[j]:= etr(shr(b[j-1])) od: a:= shr(b[7]): seq(a(n), n=0..40); # Alois P. Heinz, Sep 08 2008
  • Mathematica
    etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; b]; shr[p_] = If[# == 0, 1, p[#-1]]&; b[0] = etr[1&]; For[j = 1, j <= 7, j++, b[j] = etr[shr[b[j-1]]]]; a = shr[b[7]]; Table[a[n], {n, 0, 31}] (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *)

Formula

Take Euler transform of A034825 and shift right. (Christian G. Bower).

A126085 Number of n-node rooted trees of height 9.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 53, 251, 1043, 3961, 14102, 47816, 156129, 494769, 1530583, 4642490, 13853571, 40779959, 118666510, 341938083, 977028128, 2771407719, 7811504825, 21895173627, 61069528116, 169590519864, 469117076770
Offset: 1

Views

Author

N. J. A. Sloane, Mar 02 2007

Keywords

Links

Crossrefs

Column h=9 of A034781.

Programs

  • Maple
    For Maple program see link in A000235.
Previous Showing 11-15 of 15 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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