A227819 -id:A227819 - cp's OEIS frontend

A038092 Number of n-node rooted identity trees of height 8.

1, 7, 27, 82, 221, 553, 1323, 3078, 7019, 15765, 34992, 76922, 167697, 363020, 780937, 1670786, 3557060, 7539856, 15918972, 33490067, 70226358, 146822144, 306121101, 636648253, 1320964417, 2734901341, 5650875038, 11653922283, 23991828701, 49310264440

Offset: 9

Christian G. Bower, Jan 04 1999

The number of terms with a(n)>0 is A038093(8) - 8. - Alois P. Heinz, Sep 22 2013

Alois P. Heinz, Table of n, a(n) for n = 9..1000
Index entries for sequences related to rooted trees

Cf. A038081-A038093.

Column k=8 of A227819.

f[n_]:=Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]],{i,1,Length[#]}],{x,0,50}],x]&,{1},n];Drop[f[8]-PadRight[f[7],Length[f[8]]],8] (* Geoffrey Critzer, Aug 01 2013 *)

A038087-A038086.

A229403 Number of n-node rooted identity trees of height 9.

Original entry on oeis.org

1, 8, 35, 118, 347, 937, 2396, 5913, 14232, 33628, 78354, 180562, 412369, 934692, 2105002, 4714008, 10504530, 23304653, 51497811, 113391278, 248863010, 544569597, 1188413271, 2587000060, 5618544541, 12176514816, 26336600045, 56858108011, 122538855414

Offset: 10

Alois P. Heinz, Sep 22 2013

The number of terms with a(n)>0 is A038093(9)-9.

Alois P. Heinz, Table of n, a(n) for n = 10..500

Column k=9 of A227819.

A229404 Number of n-node rooted identity trees of height 10.

Original entry on oeis.org

1, 9, 44, 163, 519, 1502, 4081, 10625, 26836, 66278, 160934, 385647, 914426, 2149634, 5017105, 11638062, 26853653, 61674487, 141063327, 321453345, 730085764, 1653165271, 3733016952, 8408241791, 18894670248, 42368155842, 94814369316, 211789296206, 472262524451

Offset: 11

Alois P. Heinz, Sep 22 2013

The number of terms with a(n)>0 is A038093(10)-10.

Alois P. Heinz, Table of n, a(n) for n = 11..500

Column k=10 of A227819.

A245090 Number of 2n-node rooted identity trees of height n.

Original entry on oeis.org

0, 1, 1, 2, 8, 34, 149, 672, 3078, 14232, 66278, 310408, 1460390, 6896417, 32668860, 155166468, 738679240, 3523549192, 16837094932, 80580576022, 386187326865, 1853144445292, 8902504243912, 42811658101548, 206072505914938, 992778384676916, 4786621055083592

Offset: 0

Alois P. Heinz, Jul 11 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..125

Cf. A227819.

a(n) = A227819(2n,n).

a(n) ~ c * d^n / sqrt(n), where d = 4.9159375028212..., c = 0.025641919495... . - Vaclav Kotesovec, Jul 12 2014

A245091 Number of (2n+1)-node rooted identity trees of height n.

Original entry on oeis.org

1, 0, 0, 2, 12, 61, 301, 1460, 7019, 33628, 160934, 770109, 3686706, 17661288, 84675601, 406319271, 1951428049, 9380072046, 45124798445, 217252113080, 1046731684143, 5046754081095, 24348794377704, 117547968556766, 567818803946292, 2744396907325759

Offset: 0

Alois P. Heinz, Jul 11 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..300

Cf. A227819.

a(n) = A227819(2n+1,n).

a(n) ~ c * d^n / sqrt(n), where d = 4.9159375028212... (same as for A245090), c = 0.076188269997... . - Vaclav Kotesovec, Jul 12 2014

cp's OEIS Frontend

A038092 Number of n-node rooted identity trees of height 8.

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A229403 Number of n-node rooted identity trees of height 9.

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A229404 Number of n-node rooted identity trees of height 10.

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A245090 Number of 2n-node rooted identity trees of height n.

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A245091 Number of (2n+1)-node rooted identity trees of height n.

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