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A154982 Polynomial recursion:m=0; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2). 0
1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 18, 50, 18, 1, 1, 35, 212, 212, 35, 1, 1, 68, 823, 2024, 823, 68, 1, 1, 133, 3131, 16415, 16415, 3131, 133, 1, 1, 262, 11968, 124890, 291902, 124890, 11968, 262, 1, 1, 519, 46278, 938394, 4619032, 4619032, 938394, 46278, 519 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 6, 20, 88, 496, 3808, 39360, 566144, 11208448, 312282624,...}.

LINKS

Table of n, a(n) for n=0..53.

FORMULA

m=0; 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, 4, 1},

{1, 9, 9, 1},

{1, 18, 50, 18, 1},

{1, 35, 212, 212, 35, 1},

{1, 68, 823, 2024, 823, 68, 1},

{1, 133, 3131, 16415, 16415, 3131, 133, 1},

{1, 262, 11968, 124890, 291902, 124890, 11968, 262, 1},

{1, 519, 46278, 938394, 4619032, 4619032, 938394, 46278, 519, 1},

{1, 1032, 180941, 7112288, 69501106, 158691888, 69501106, 7112288, 180941, 1032, 1}

MATHEMATICA

Clear[p, n, m, x]; m = 0; 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: A259333 A180960 A157192 * A146767 A146955 A155451

Adjacent sequences:  A154979 A154980 A154981 * A154983 A154984 A154985

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 18 2009

STATUS

approved

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)