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.

Showing 1-3 of 3 results.

A293264 Coefficients in asymptotic expansion of sequence A293251.

Original entry on oeis.org

1, -2, -2, -5, -29, -232, -2231, -24745, -308917, -4279945, -65179552, -1082598411, -19480497765, -377583928402, -7844313743160, -173920273954426, -4099686000487330, -102398103973448577, -2701860620027906307, -75107104456422563041, -2194183661233574578401
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 04 2017

Keywords

Examples

			A293251(n) / (-n!) ~ 1 - 2/n - 2/n^2 - 5/n^3 - 29/n^4 - 232/n^5 - ...

Links

Crossrefs

Cf. A293251.

A293259 G.f.: Product_{i>0} 1/(Sum_{j>=0} (-1)^j*j!*x^(j*i)).

Original entry on oeis.org

1, 1, 0, 5, -13, 75, -465, 3509, -29492, 276310, -2854776, 32242512, -395295109, 5230184477, -74303722489, 1128399929626, -18245417102767, 313000130900207, -5678742973964699, 108649510570970878, -2186444702147475131, 46169315317847827548
Offset: 0

Views

Author

Seiichi Manyama, Oct 04 2017

Keywords

Links

Crossrefs

Cf. A293236, A293251.

Programs

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

Formula

Convolution inverse of A293236.
a(n) ~ -(-1)^n * n! * (1 - 2/n - 7/n^3 - 39/n^4 - 272/n^5 - 2457/n^6 - 26443/n^7 - 324675/n^8 - 4453439/n^9 - 67360840/n^10), for coefficients see A293265. - Vaclav Kotesovec, Oct 04 2017

A293285 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} j!*x^(j*i)).

Original entry on oeis.org

1, 1, 0, 1, -1, 0, 1, -1, 0, 0, 1, -1, -2, -1, 0, 1, -1, -2, 3, 1, 0, 1, -1, -2, -3, -1, -1, 0, 1, -1, -2, -3, 11, -5, 1, 0, 1, -1, -2, -3, -13, 7, 9, -1, 0, 1, -1, -2, -3, -13, 55, -15, 3, 2, 0, 1, -1, -2, -3, -13, -65, 33, -63, -20, -2, 0, 1, -1, -2, -3, -13, -65
Offset: 0

Views

Author

Seiichi Manyama, Oct 04 2017

Keywords

Examples

			Square array begins:
   1,  1,  1,  1,   1, ...
   0, -1, -1, -1,  -1, ...
   0,  0, -2, -2,  -2, ...
   0, -1,  3, -3,  -3, ...
   0,  1, -1, 11, -13, ...
   0, -1, -5,  7,  55, ...

Links

Crossrefs

Columns k=0..2 give A000007, A081362, A293287.
Rows n=0..1 give A000012, (-1)*A057427.
Main diagonal gives A293251.
Cf. A293202, A293293.
Showing 1-3 of 3 results.

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

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