login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322268 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(x)*(sec(x) + tan(x))^k. 2
1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 9, 1, 1, 5, 16, 29, 24, 1, 1, 6, 25, 67, 105, 77, 1, 1, 7, 36, 129, 304, 433, 294, 1, 1, 8, 49, 221, 705, 1519, 2029, 1309, 1, 1, 9, 64, 349, 1416, 4145, 8386, 10709, 6664, 1, 1, 10, 81, 519, 2569, 9601, 26385, 51007, 63025, 38177, 1, 1, 11, 100, 737, 4320, 19777, 69406, 181969, 340024, 409713, 243034, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..77.

Index entries for sequences related to boustrophedon transform

FORMULA

E.g.f. of column k: exp(x)*(sec(x) + tan(x))^k.

EXAMPLE

E.g.f. of column k: A_k(x) = 1 + (k + 1)*x/1! + (k + 1)^2*x^2/2! + (k^3 + 3*k^2 + 4*k + 1)*x^3/3! + (k^4 + 4*k^3 + 10*k^2 + 8*k + 1)*x^4/4! + ...

Square array begins:

  1,   1,    1,     1,     1,     1,  ...

  1,   2,    3,     4,     5,     6,  ...

  1,   4,    9,    16,    25,    36,  ...

  1,   9,   29,    67,   129,   221,  ...

  1,  24,  105,   304,   705,  1416,  ...

  1,  77,  433,  1519,  4145,  9601,  ...

MATHEMATICA

Table[Function[k, n! SeriesCoefficient[Exp[x] (Sec[x] + Tan[x])^k, {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten

CROSSREFS

Columns k=0..3 give A000012, A000667, A292756, A292759.

Main diagonal gives A296793.

Cf. A322267.

Sequence in context: A071922 A138028 A009999 * A144823 A098446 A098447

Adjacent sequences:  A322265 A322266 A322267 * A322269 A322270 A322271

KEYWORD

nonn,tabl

AUTHOR

Ilya Gutkovskiy, Dec 01 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 14:37 EST 2019. Contains 329999 sequences. (Running on oeis4.)