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A154980 Polynomial recursion:m=1; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2). 0
1, 1, 1, 1, 6, 1, 1, 15, 15, 1, 1, 32, 126, 32, 1, 1, 65, 638, 638, 65, 1, 1, 130, 2751, 9340, 2751, 130, 1, 1, 259, 11201, 93755, 93755, 11201, 259, 1, 1, 516, 44740, 809212, 2578550, 809212, 44740, 516, 1, 1, 1029, 177864, 6588864, 51390322, 51390322 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 8, 32, 192, 1408, 15104, 210432, 4287488, 116316160, 4623020032,...}.

LINKS

Table of n, a(n) for n=0..50.

FORMULA

m=1; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2);

t(n,m)=coefficients(p(x,n))

EXAMPLE

{1},

{1, 1},

{1, 6, 1},

{1, 15, 15, 1},

{1, 32, 126, 32, 1},

{1, 65, 638, 638, 65, 1},

{1, 130, 2751, 9340, 2751, 130, 1},

{1, 259, 11201, 93755, 93755, 11201, 259, 1},

{1, 516, 44740, 809212, 2578550, 809212, 44740, 516, 1},

{1, 1029, 177864, 6588864, 51390322, 51390322, 6588864, 177864, 1029, 1},

{1, 2054, 707277, 52580488, 886612274, 2743215844, 886612274, 52580488, 707277, 2054, 1}

MATHEMATICA

Clear[p, n, m, x]; m = 1; p[x, 0] = 1; p[x, 1] = x + 1;

p[x_, n_] := p[x, n] = (x + 1)*p[x, n - 1] + 2^(m + n - 1)*x*p[x, n - 2];

Table[ExpandAll[p[x, n]], {n, 0, 10}];

Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A295985 A086645 A168291 * A166344 A146766 A176152

Adjacent sequences:  A154977 A154978 A154979 * A154981 A154982 A154983

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

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Last modified April 20 04:42 EDT 2019. Contains 322294 sequences. (Running on oeis4.)