A247855 The 10th Hermite Polynomial evaluated at n: H_10(n) = 1024*n^10 - 23040*n^8 + 161280*n^6 - 403200*n^4 + 302400*n^2 - 30240.

-30240, 8224, 200416, -3093984, 125984224, 3275529760, 30232000224, 174454774816, 753610971616, 2661760648224, 8093278209760, 21900944840224, 53969864949216, 123139662877216, 263393520320224, 533257736009760, 1029623343008224, 1907515621443616

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Hermite Polynomial

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1)

Formula

G.f.: (-30240+340864*x-1553248*x^2+143360*x^3+159704768*x^4 +1703150336*x^5+1689179456*x^6+169683968*x^7-4846240*x^8 +109952*x^9+8224*x^10)/(1-x)^11.

a(n) = 11*a(n-1)-55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)-165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11).

Mathematica

Table[1024 n^10 - 23040 n^8 + 161280 n^6 - 403200 n^4 + 302400 n^2 - 30240, {n, 0, 30}] (* or *) CoefficientList[Series[(-30240 + 340864 x - 1553248 x^2 + 143360 x^3 + 159704768 x^4 + 1703150336 x^5 + 1689179456 x^6 + 169683968 x^7 - 4846240 x^8 + 109952 x^9 + 8224 x^10)/(1-x)^11, {x, 0, 30}], x]

Prog

(Magma) [1024*n^10-23040*n^8+161280*n^6-403200*n^4 +302400*n^2-30240: n in [0..30]]; /* or */ I:=[-30240, 8224, 200416, -3093984, 125984224, 3275529760, 30232000224, 174454774816, 753610971616, 2661760648224, 8093278209760]; [n le 11 select I[n] else 11*Self(n-1)-55*Self(n-2)+165*Self(n-3)-330*Self(n-4)+462*Self(n-5)-462*Self(n-6)+330*Self(n-7)-165*Self(n-8)+55*Self(n-9)-11*Self(n-10)+Self(n-11): n in [1..30]];
(Python)
m = [3715891200, -16721510400, 30036787200, -27095040000, 12533391360, -2612736000, 139499520, 3640320, 153728, -38464, -30240]
A247855_list = [m[-1]]
for _ in range(10**1):
....for i in range(10):
........m[i+1]+= m[i]
....A247855_list.append(m[-1]) # Chai Wah Wu, Nov 09 2014
(PARI) a(n)=polhermite(10, n) \\ Charles R Greathouse IV, Jan 29 2016

Crossrefs

Cf. similar sequences listed in A247850.

Sequence in context: A255759 A255752 A254841 * A113286 A355279 A027687

Adjacent sequences: A247852 A247853 A247854 * A247856 A247857 A247858

Keyword

sign,easy

Author

Vincenzo Librandi, Sep 26 2014

Status

approved