A124551 -id:A124551 - cp's OEIS frontend

A124565 Row 5 of table A124560; also, the self-convolution 5th power equals A124555, which is row 5 of table A124550.

1, 1, 6, 51, 556, 7581, 128532, 2689248, 68880819, 2155007000, 82603481941, 3896490943878, 227153148813546, 16429403864272555, 1478934508425795630, 166091860417795409081, 23316582876166010185959

Offset: 0

Paul D. Hanna, Nov 07 2006

nonn

In table A124560, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k * [R_{n*k}(y)]^(n*k) for n>=0.

Cf. A124560 (table); other rows: A124551, A124562, A124563, A124564, A124566.

G.f.: A(x) = Sum_{k>=0} y^k * [R_{5k}(y)]^(5k), where R_n(x) is the g.f. of row n in table A124560.

A124566 Row 6 of table A124560; also, the self-convolution 6th power equals A124556, which is row 6 of table A124550.

Original entry on oeis.org

1, 1, 7, 70, 891, 14036, 272914, 6525900, 190604859, 6781448755, 294798563020, 15737487680990, 1036588563202854, 84606134756948277, 8587502188940359207, 1086820294948914428468, 171866738763640156327659

Offset: 0

Paul D. Hanna, Nov 07 2006

nonn

In table A124560, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k * [R_{n*k}(y)]^(n*k) for n>=0.

Cf. A124560 (table); other rows: A124551, A124562, A124563, A124564, A124565.

G.f.: A(x) = Sum_{k>=0} y^k * [R_{6k}(y)]^(6k), where R_n(x) is the g.f. of row n in table A124560.

A124557 Main diagonal of table A124550.

Original entry on oeis.org

1, 1, 7, 91, 1899, 57876, 2447115, 139777303, 10629219251, 1066463205220, 140409644914798, 24185696469330452, 5439617764120907676, 1594552369099740836202, 608364562372792302094447

Offset: 0

Paul D. Hanna, Nov 07 2006

nonn

In table A124550, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k * R_{n*k}(y) ]^n for n>=0.

Cf. A124550 (table); A124558, A124559; A124551, A124552, A124554, A124555, A124556.

A124558 Secondary diagonal of table A124550; a(n) = A124550(n+1,n).

Original entry on oeis.org

1, 2, 15, 204, 4345, 133212, 5621371, 319211576, 24097683942, 2399637270890, 313606810455697, 53638534570897308, 11984755429488415041, 3491974842611221434342, 1324861497596788043284935

Offset: 0

Paul D. Hanna, Nov 07 2006

nonn

In table A124550, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k * R_{n*k}(y) ]^n for n>=0.

Cf. A124550 (table); A124557, A124559; A124551, A124552, A124554, A124555, A124556.

a(n) is divisible by (n+1): A124559(n) = a(n)/(n+1).

A124559 Derived from secondary diagonal of table A124550; a(n) = A124550(n+1,n)/(n+1).

Original entry on oeis.org

1, 1, 5, 51, 869, 22202, 803053, 39901447, 2677520438, 239963727089, 28509710041427, 4469877880908109, 921904263806801157, 249426774472230102453, 88324099839785869552329

Offset: 0

Paul D. Hanna, Nov 07 2006

nonn

In table A124550, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k * R_{n*k}(y) ]^n for n>=0.

Cf. A124550 (table); A124557, A124558; A124551, A124552, A124554, A124555, A124556.

a(n) = (n+1)*A124558(n).

A124568 Triangle, read by rows, where row n equals the inverse binomial transform of the column n in rectangular table A124550 (starting with row 1).

Original entry on oeis.org

1, 1, 1, 2, 5, 3, 5, 25, 36, 16, 16, 143, 364, 362, 125, 66, 990, 3909, 6417, 4728, 1296, 348, 8464, 48518, 116274, 135932, 76867, 16807, 2321, 89741, 720078, 2370938, 3923330, 3441366, 1518460, 262144, 19437, 1180978, 12965026, 56627440

Offset: 0

Paul D. Hanna, Nov 08 2006

			Triangle begins:
1;
1, 1;
2, 5, 3;
5, 25, 36, 16;
16, 143, 364, 362, 125;
66, 990, 3909, 6417, 4728, 1296;
348, 8464, 48518, 116274, 135932, 76867, 16807;
2321, 89741, 720078, 2370938, 3923330, 3441366, 1518460, 262144; ...

Cf. A124550, A124551, A000272.

T(n,n) = (n+1)^(n-1) = A000272(n+1). T(n,0) = A124551(n).

cp's OEIS Frontend

A124565 Row 5 of table A124560; also, the self-convolution 5th power equals A124555, which is row 5 of table A124550.

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A124566 Row 6 of table A124560; also, the self-convolution 6th power equals A124556, which is row 6 of table A124550.

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A124557 Main diagonal of table A124550.

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A124558 Secondary diagonal of table A124550; a(n) = A124550(n+1,n).

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A124559 Derived from secondary diagonal of table A124550; a(n) = A124550(n+1,n)/(n+1).

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A124568 Triangle, read by rows, where row n equals the inverse binomial transform of the column n in rectangular table A124550 (starting with row 1).

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