login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
2
-30240, 8224, 200416, -3093984, 125984224, 3275529760, 30232000224, 174454774816, 753610971616, 2661760648224, 8093278209760, 21900944840224, 53969864949216, 123139662877216, 263393520320224, 533257736009760, 1029623343008224, 1907515621443616
OFFSET
0,1
LINKS
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
KEYWORD
sign,easy
AUTHOR
Vincenzo Librandi, Sep 26 2014
STATUS
approved