A293259 -id:A293259 - cp's OEIS frontend

A293265 Coefficients in asymptotic expansion of sequence A293259.

1, -2, 0, -7, -39, -272, -2457, -26443, -324675, -4453439, -67360840, -1113125559, -19949867987, -385450438438, -7987089578144, -176710071650036, -4158070097543962, -103700987989612861, -2732746882427265825, -75882355625448093577, -2214726801268428430553

Offset: 0

Vaclav Kotesovec, Oct 04 2017

sign

			A293259(n) / (-(-1)^n * n!) ~ 1 - 2/n - 7/n^3 - 39/n^4 - 272/n^5 - ...

Vaclav Kotesovec, Table of n, a(n) for n = 0..28

Cf. A293259.

A293251 G.f.: Product_{i>0} 1/(Sum_{j>=0} j!x^(ji)).

Original entry on oeis.org

1, -1, -2, -3, -13, -65, -447, -3351, -28544, -269270, -2795872, -31689198, -389581679, -5165672203, -73512910689, -1117937393138, -18096787251877, -310743077434399, -5642249024063207, -108023468997424550, -2175086628366359447, -45952007357795606912

Offset: 0

Seiichi Manyama, Oct 04 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..449

Cf. A161779, A293259.

nmax = 30; CoefficientList[Series[Product[1/Sum[j!*x^(j*k), {j, 0, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 04 2017 *)

Convolution inverse of A161779.

a(n) ~ -n! * (1 - 2/n - 2/n^2 - 5/n^3 - 29/n^4 - 232/n^5 - 2231/n^6 - 24745/n^7 - 308917/n^8 - 4279945/n^9 - 65179552/n^10), for coefficients see A293264. - Vaclav Kotesovec, Oct 04 2017

A293293 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(Sum_{j=0..k} (-1)^jj!x^(j*i)).

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 0, 3, 0, 1, 1, 0, -1, 5, 0, 1, 1, 0, 5, -1, 7, 0, 1, 1, 0, 5, 11, 3, 11, 0, 1, 1, 0, 5, -13, 3, 3, 15, 0, 1, 1, 0, 5, -13, -45, 15, -1, 22, 0, 1, 1, 0, 5, -13, 75, 15, 77, -8, 30, 0, 1, 1, 0, 5, -13, 75, 255, -91, 76, -8, 42, 0

Offset: 0

Seiichi Manyama, Oct 05 2017

			Square array begins:
   1, 1,  1,  1,   1, ...
   0, 1,  1,  1,   1, ...
   0, 2,  0,  0,   0, ...
   0, 3, -1,  5,   5, ...
   0, 5, -1, 11, -13, ...
   0, 7,  3,  3, -45, ...

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Columns k=0..2 give A000007, A000041, A293294.
Rows n=0..1 give A000012, A057427.
Main diagonal gives A293259.
Cf. A293071, A293285.

cp's OEIS Frontend

A293265 Coefficients in asymptotic expansion of sequence A293259.

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A293251 G.f.: Product_{i>0} 1/(Sum_{j>=0} j!x^(ji)).

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A293293 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(Sum_{j=0..k} (-1)^jj!x^(j*i)).

Views

Author

Keywords

Examples

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Crossrefs

cp's OEIS Frontend

A293265 Coefficients in asymptotic expansion of sequence A293259.

Views

Author

Keywords

Examples

Links

Crossrefs

A293251 G.f.: Product_{i>0} 1/(Sum_{j>=0} j!*x^(j*i)).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A293293 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(Sum_{j=0..k} (-1)^j*j!*x^(j*i)).

Views

Author

Keywords

Examples

Links

Crossrefs

A293251 G.f.: Product_{i>0} 1/(Sum_{j>=0} j!x^(ji)).

A293293 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(Sum_{j=0..k} (-1)^jj!x^(j*i)).