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A156139 Triangle A(n,1)=A(n,n)=1; A(n,k) = (2*n-k-1) *A(n-1,k-1) + (k+1)*A(n-1,k) read by rows, 1<=k<=n. 3
1, 1, 1, 1, 6, 1, 1, 23, 28, 1, 1, 76, 250, 145, 1, 1, 237, 1608, 2475, 876, 1, 1, 722, 8802, 26847, 25056, 6139, 1, 1, 2179, 43872, 231057, 418806, 268477, 49120, 1, 1, 6552, 205994, 1725621, 5285520, 6486205, 3077730, 442089, 1, 1, 19673, 928808 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are s(n) = 1, 2, 8, 53, 473, 5198, 67568, 1013513, 17229713, 327364538,...

LINKS

Table of n, a(n) for n=1..48.

Leonard M. Smiley, Completion of a Rational Function Sequence of Carlitz, page 2.

FORMULA

Row sums s(n) = sum{k=1..n} A(n,k) seem to obey (n-2)*s(n) -(1-4*n+2*n^2)*s(n-1) +(3-5*n+2*n^2) *s(n-2)=0, n>0. - R. J. Mathar, Jun 24 2011

EXAMPLE

1;

1, 1;

1, 6, 1;

1, 23, 28, 1;

1, 76, 250, 145, 1;

1, 237, 1608, 2475, 876, 1;

1, 722, 8802, 26847, 25056, 6139, 1;

1, 2179, 43872, 231057, 418806, 268477, 49120, 1;

1, 6552, 205994, 1725621, 5285520, 6486205, 3077730, 442089, 1;

1, 19673, 928808, 11718015, 55871814, 114115195, 102456300, 37833831, 4420900, 1;

MAPLE

A156139 := proc(n, k) option remember; if k= 1 or k=n then 1; else (2*n-k-1)*procname(n-1, k-1)+(k+1)*procname(n-1, k) ; end if; end proc:

seq(seq(A156139(n, k), k=1..n), n=1..10) ; # R. J. Mathar, Jun 24 2011

MATHEMATICA

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

A[n_, k_] := (2*n - k - 1)*A[n - 1, k - 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: A138076 A060187 A174527 * A155863 A173882 A174045

Adjacent sequences:  A156136 A156137 A156138 * A156140 A156141 A156142

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 04 2009

STATUS

approved

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Last modified February 17 14:12 EST 2018. Contains 299296 sequences. (Running on oeis4.)