login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A156576 A triangular sequence of the antidiagonal of the q squared like factorial: t(n,m)=If[m == 0, n!, Product[Sum[(i + 1)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]. 0
1, 1, 1, 1, 1, 2, 1, 1, 5, 6, 1, 1, 7, 85, 24, 1, 1, 9, 238, 4165, 120, 1, 1, 11, 513, 33796, 537285, 720, 1, 1, 13, 946, 160569, 18486412, 172468485, 5040, 1, 1, 15, 1573, 554356, 255786417, 37065256060, 132628264965, 40320, 1, 1, 17, 2430, 1549405 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums are:

{1, 2, 4, 13, 118, 4534, 572327, 191121467, 169949903708, 503243397794904,

7528543001953603041,...}.

The q squared binomials turn out rational.

Based on polynomials:

p(x,n) =(1-x)^2*Sum[(k + 1)*(x)^k, {k, 0, n - 1}];

where:

q(x,n)= Sum[(k + 1)*(x)^k, {k, 0, n - 1}];

is a count up polynomial.

LINKS

Table of n, a(n) for n=0..49.

FORMULA

t(n,m)=If[m == 0, n!, Product[Sum[(i + 1)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]];

out_(n,m)=antidiagonal(t(n,m))

EXAMPLE

{1},

{1, 1},

{1, 1, 2},

{1, 1, 5, 6},

{1, 1, 7, 85, 24},

{1, 1, 9, 238, 4165, 120},

{1, 1, 11, 513, 33796, 537285, 720},

{1, 1, 13, 946, 160569, 18486412, 172468485, 5040},

{1, 1, 15, 1573, 554356, 255786417, 37065256060, 132628264965, 40320},

{1, 1, 17, 2430, 1549405, 2057215116, 1979019508329, 263459840074480, 237802479082245, 362880},

{1, 1, 19, 3553, 3727620, 11566308325, 46207108720476, 72054121278750561, 6482165905192505920, 974276756799957765, 3628800}

MATHEMATICA

Clear[t, n, m, i, k, a, b];

t[n_, m_] = If[m == 0, n!, Product[Sum[(i + 1)*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];

a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}];

b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}];

Flatten[%]

CROSSREFS

Sequence in context: A086856 A052916 A326048 * A293219 A266572 A266681

Adjacent sequences:  A156573 A156574 A156575 * A156577 A156578 A156579

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 10 2009

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 February 21 05:23 EST 2020. Contains 332086 sequences. (Running on oeis4.)