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A156136 A triangle of polynomial coefficients related to Mittag-Leffler polynomials: p(x,n)=Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x). 1
1, 2, 2, 3, 12, 4, 4, 36, 48, 8, 5, 80, 240, 160, 16, 6, 150, 800, 1200, 480, 32, 7, 252, 2100, 5600, 5040, 1344, 64, 8, 392, 4704, 19600, 31360, 18816, 3584, 128, 9, 576, 9408, 56448, 141120, 150528, 64512, 9216, 256, 10, 810, 17280, 141120, 508032 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 75-76

LINKS

Table of n, a(n) for n=0..49.

FORMULA

p(x,n)=Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x);

p(x,n)=n Hypergeometric2F1[1 - n, 1 - n, 2, 2 x];

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

T(n,m) = 2^m*A103371(n,m). - R. J. Mathar, Dec 05 2017

EXAMPLE

1;

2, 2;

3, 12, 4;

4, 36, 48, 8;

5, 80, 240, 160, 16;

6, 150, 800, 1200, 480, 32;

7, 252, 2100, 5600, 5040, 1344, 64;

8, 392, 4704, 19600, 31360, 18816, 3584, 128;

9, 576, 9408, 56448, 141120, 150528, 64512, 9216, 256;

10, 810, 17280, 141120, 508032, 846720, 645120, 207360, 23040, 512;

MATHEMATICA

Clear[t0, p, x, n, m];

p[x_, n_] = Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x);

Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}];

Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}];

Flatten[%]

CROSSREFS

A142983, A142978, A047781 (row sums).

Sequence in context: A246670 A075095 A178343 * A134243 A182779 A199673

Adjacent sequences:  A156133 A156134 A156135 * A156137 A156138 A156139

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 04 2009

STATUS

approved

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Last modified October 23 16:46 EDT 2019. Contains 328373 sequences. (Running on oeis4.)