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a(n) = 24*(n^1 + 1!)*(n^2 + 2!)*(n^3 + 3!)*...*(n^6 + 6!)/6!.
2

%I #7 Apr 15 2015 17:14:14

%S 829440,3053435,40040448,2673065934,323958835200,24350583830265,

%T 971969903106048,23061845117771260,365309311365605376,

%U 4216355578004498775,37787143366734755840,275548505246977513866,1693398609738955671552,9010265266941299501973,42393383140543522560000

%N a(n) = 24*(n^1 + 1!)*(n^2 + 2!)*(n^3 + 3!)*...*(n^6 + 6!)/6!.

%H Colin Barker, <a href="/A131684/b131684.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: -(1103872*x^20 -312478243*x^19 -120671064318*x^18 -10924415464963*x^17 -365289416188928*x^16 -5416497937794108*x^15 -40283003777941144*x^14 -162386613652960172*x^13 -372036568602512352*x^12 -497148917411217834*x^11 -390969147820033860*x^10 -179789868762494298*x^9 -47275965677665472*x^8 -6823180930101292*x^7 -507249401959608*x^6 -17779798800764*x^5 -275765791840*x^4 -1220181963*x^3 -164465518*x^2 +15194245*x -829440) / (x -1)^22. - _Colin Barker_, Apr 15 2015

%o (PARI) a(n) = 24*prod(k=1, 6, n^k + k!)/6!; \\ _Michel Marcus_, Apr 15 2015

%Y See A049614.

%K nonn,easy

%O 0,1

%A _Alexander R. Povolotsky_, Aug 29 2007