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A171636 Coefficients of Lommel polynomials:n=m;p(x,n,m)=(Gamma[n + m]/(Gamma[n] ((z/ 2))^m)) HypergeometricPFQ[{((1 - m))/2, (-m)/2}, {n, (-m), 1 - n - m}, z^2] 0
2, 24, 0, 1, 480, 0, 16, 13440, 0, 360, 0, 1, 483840, 0, 10752, 0, 42, 21288960, 0, 403200, 0, 1728, 0, 1, 1107025920, 0, 18247680, 0, 79200, 0, 80, 66421555200, 0, 968647680, 0, 4118400, 0, 5280, 0, 1, 4516665753600, 0, 59041382400, 0, 242161920 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are: 2, 25, 496, 13801, 494634, 21693889, 1125352880, 67394326561, 4575949647490, 347347588935481

LINKS

Table of n, a(n) for n=1..45.

Weisstein, Eric W. Lommel Polynomial. MathWorld.

FORMULA

n=m;p(x,n,m)=(Gamma[n + m]/(Gamma[n] ((z/ 2))^m)) HypergeometricPFQ[{((1 - m))/2, (-m)/2}, {n, (-m), 1 - n - m}, z^2]

EXAMPLE

{2},

{24, 0, 1},

{480, 0, 16},

{13440, 0, 360, 0, 1},

{483840, 0, 10752, 0, 42},

{21288960, 0, 403200, 0, 1728, 0, 1},

{1107025920, 0, 18247680, 0, 79200, 0, 80},

{66421555200, 0, 968647680, 0, 4118400, 0, 5280, 0, 1},

{4516665753600, 0, 59041382400, 0, 242161920, 0, 349440, 0, 130},

{343266597273600, 0, 4064999178240, 0, 15968010240, 0, 24460800, 0, 12600, 0, 1}

MATHEMATICA

LommelR1[m_, n_, z_] := (Gamma[n + m]/(Gamma[n] ((z/ 2))^m)) HypergeometricPFQ[{((1 - m))/2, (- m)/2}, {n, (-m), 1 - n - m}, z^2]

Table[CoefficientList[Expand[LommelR1[n, n, x]*x^n], x], {n, 1, 10}]

Flatten[%]

CROSSREFS

Sequence in context: A118812 A228241 A054909 * A270562 A100816 A079612

Adjacent sequences:  A171633 A171634 A171635 * A171637 A171638 A171639

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 13 2009

STATUS

approved

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Last modified November 26 09:38 EST 2020. Contains 338639 sequences. (Running on oeis4.)