A156137 A recursive triangle sequence: A(n,k)=k^2*(A(n - 1, k - 1) + A(n - 1, k))

1, 1, 1, 1, 8, 1, 1, 36, 81, 1, 1, 148, 1053, 1312, 1, 1, 596, 10809, 37840, 32825, 1, 1, 2388, 102645, 778384, 1766625, 1181736, 1, 1, 9556, 945297, 14096464, 63625225, 106140996, 57905113, 1, 1, 38228, 8593677, 240668176, 1943042225, 6111583956

Offset

0,5

Comments

Row sums are:

{1, 2, 10, 119, 2515, 82072, 3831780, 242722653, 20048112901, 2093775709630,...}.

This sequence resulted from reading the book Combinatorial Identities by John Riordan.

References

Review: John Riordan, Combinatorial identities,Paul R. Stein,Bull. Amer. Math. Soc. Volume 78, Number 4 (1972), 490-496.

Links

Table of n, a(n) for n=0..41.

Formula

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

Example

{1},
{1, 1},
{1, 8, 1},
{1, 36, 81, 1},
{1, 148, 1053, 1312, 1},
{1, 596, 10809, 37840, 32825, 1},
{1, 2388, 102645, 778384, 1766625, 1181736, 1},
{1, 9556, 945297, 14096464, 63625225, 106140996, 57905113, 1},
{1, 38228, 8593677, 240668176, 1943042225, 6111583956, 8038259341, 3705927296, 1},
{1, 152916, 77687145, 3988189648, 54592760025, 289966542516, 693342321553, 751627944768, 300180111057, 1}

Mathematica

A[n_, 1] := 1; A[n_, n_] := 1;
A[n_, k_] := k^2*(A[n - 1, k - 1] + A[n - 1, k]);
TableForm[Table[A[n, k], {n, 10}, {k, n}], TableAlignments -> Right];
Table[Table[A[n, k], {k, n}], {n, 10}];
Flatten[%]

Crossrefs

Sequence in context: A142467 A142175 A142597 * A152972 A166346 A157640

Adjacent sequences: A156134 A156135 A156136 * A156138 A156139 A156140

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Feb 04 2009

Status

approved