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A154229 A recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) +(n*(n + 1)/2)^2*A(n - 2, k - 1). 0
1, 1, 1, 1, 38, 1, 1, 139, 139, 1, 1, 365, 8828, 365, 1, 1, 807, 70492, 70492, 807, 1, 1, 1592, 357459, 7062136, 357459, 1592, 1, 1, 2889, 1404923, 98777227, 98777227, 1404923, 2889, 1, 1, 4915, 4631612, 824036625, 14498379854, 824036625, 4631612 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 40, 280, 9560, 142600, 7780240, 200370080, 16155726160, 638430944320,...}.

LINKS

Table of n, a(n) for n=0..42.

FORMULA

A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (n*(n + 1)/2)^2*A(n - 2, k - 1).

EXAMPLE

{1},

{1, 1},

{1, 38, 1},

{1, 139, 139, 1},

{1, 365, 8828, 365, 1},

{1, 807, 70492, 70492, 807, 1},

{1, 1592, 357459, 7062136, 357459, 1592, 1},

{1, 2889, 1404923, 98777227, 98777227, 1404923, 2889, 1},

{1, 4915, 4631612, 824036625, 14498379854, 824036625, 4631612, 4915, 1},

{1, 7941, 13375752, 5078560312, 314123528154, 314123528154, 5078560312, 13375752, 7941, 1}

MATHEMATICA

A[n_, 1] := 1; A[n_, n_] := 1;

A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n*(n + 1)/2)^2*A[n - 2, k - 1];

Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A171407 A023930 A022072 * A225433 A225398 A037936

Adjacent sequences:  A154226 A154227 A154228 * A154230 A154231 A154232

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 05 2009

STATUS

approved

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Last modified September 28 08:33 EDT 2020. Contains 337394 sequences. (Running on oeis4.)