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!)
A177851 Triangle read by rows: T(n, m) = binomial(n + m - 3, m - 1)*(2 * m + n - 2) / m, for n>=1 and 1<=m<=n. 0
1, 2, 2, 3, 5, 7, 4, 9, 16, 25, 5, 14, 30, 55, 91, 6, 20, 50, 105, 196, 336, 7, 27, 77, 182, 378, 714, 1254, 8, 35, 112, 294, 672, 1386, 2640, 4719, 9, 44, 156, 450, 1122, 2508, 5148, 9867, 17875, 10, 54, 210, 660, 1782, 4290, 9438, 19305, 37180, 68068 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This triangle sequence is the number of linearly independent homogeneous harmonic polynomials of degree m in n variables.

REFERENCES

Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, page 170

LINKS

Table of n, a(n) for n=1..55.

FORMULA

Row sums are ((3*n-1)*binomial(2*n-2,n)/(n-1)-1) for n>=2.

{1, 4, 15, 54, 195, 713, 2639, 9866, 37179, 140997,...}.

EXAMPLE

Triangle starts:

{1},

{2, 2},

{3, 5, 7},

{4, 9, 16, 25},

{5, 14, 30, 55, 91},

{6, 20, 50, 105, 196, 336},

{7, 27, 77, 182, 378, 714, 1254},

{8, 35, 112, 294, 672, 1386, 2640, 4719},

{9, 44, 156, 450, 1122, 2508, 5148, 9867, 17875},

{10, 54, 210, 660, 1782, 4290, 9438, 19305, 37180, 68068.

MAPLE

T := (n, m) -> ((2*m + n - 2)/m)*binomial(n + m - 3, m - 1):

for n from 1 to 10 do lprint(seq(T(n, k), k=1..n)) od; # Peter Luschny, Dec 16 2015

MATHEMATICA

Flatten[Table[Table[((2*m + n - 2)/m)*Binomial[n + m - 3, m - 1], {m, 1, n}], {n, 1, 10}]]

CROSSREFS

Sequence in context: A139074 A179418 A035428 * A100142 A245935 A178880

Adjacent sequences:  A177848 A177849 A177850 * A177852 A177853 A177854

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, May 14 2010

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 26 03:29 EST 2020. Contains 332273 sequences. (Running on oeis4.)