login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123243 Triangular array: odd: p(k, x) = 2*x*p(k-1, x) + (1-x2)*p(k-2, x), even: p(k, x) = (Sum_{m=0..k} x^m)*p(k-1, x). 0
1, 1, 1, 2, 1, 2, 3, 3, 3, 1, 12, 16, 17, 18, 6, 12, 28, 45, 63, 69, 69, 57, 41, 24, 6, 120, 268, 434, 613, 672, 684, 570, 410, 240, 60, 120, 388, 822, 1435, 2107, 2791, 3361, 3771, 3891, 3683, 3249, 2636, 1964, 1280, 710, 300, 60, 1680, 5312, 11240, 19656, 28885 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
REFERENCES
E. S. R. Gopal, Specific Heats at Low Temperatures, Plenum Press, New York, 1966, pages 36-40
S. M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New York, 1960, page 110
LINKS
B. H. Margolius, Permutations with inversions, J. Integ. Seqs. Vol. 4 (2001), #01.2.4.
FORMULA
odd: p(k, x) = 2*x*p(k-1, x) + (1-x2)*p(k-2, x);
even: p(k, x) = (Sum_{m=0..k} x^m)*p(k-1, x)
EXAMPLE
{1},
{1, 1},
{2, 1},
{2, 3, 3, 3, 1},
{12, 16, 17, 18, 6},
{12, 28, 45, 63, 69, 69, 57, 41, 24, 6},
{120, 268, 434, 613, 672, 684, 570, 410, 240, 60},
{120, 388, 822, 1435, 2107, 2791, 3361, 3771, 3891, 3683, 3249, 2636, 1964, 1280, 710, 300, 60}
MATHEMATICA
p[0, x] = 1; p[1, x] = x + 1;
p[k_, x_] := p[k, x] = If[Mod[k, 2] == 0, 2*(k - 1)*p[k - 1, x] - x*p[k - 2, x], Sum[x^m, {m, 0, k}]*p[k - 1, x]];
w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
CROSSREFS
Cf. A008302.
Sequence in context: A244516 A363264 A002339 * A037193 A291615 A361789
KEYWORD
nonn,uned,tabf
AUTHOR
Roger L. Bagula, Oct 07 2006
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 28 07:05 EST 2024. Contains 370387 sequences. (Running on oeis4.)