A131676 a(n) = (Product_{i=1..6} n^i+i) / 6!.
1, 7, 14245, 28405300, 9191136045, 886286703456, 38188743738145, 932714257963020, 14966184483875625, 173860405001195185, 1563721100613810061, 11427034989921521488, 70319024498214551605, 374482754394635213250, 1763001772206469563945, 7462412915610398239816
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).
Crossrefs
Cf. A131685.
Programs
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Mathematica
Table[Product[ n^i + i, {i, 1, 6}]/6!, {n, 0, 15}] (* Michael De Vlieger, Jan 03 2016 *) -
PARI
A131676(n, k=6)=prod(i=1, k, (n^i+i))/k! \\ Changing the optional 2nd argument allows one to produce A000027 (k=1), A064808 (k=2), A131509 (k=3), A129995 (k=4), A131675 (k=5), ..., A131680 (k=10). - M. F. Hasler, May 02 2015
Formula
G.f.: (1 - 15*x + 14322*x^2 + 28091987*x^3 + 8569506575*x^4 + 690621422337*x^5 + 20769948618958*x^6 + 283347184706283*x^7 + 1969675285865562*x^8 + 7493939424807955*x^9 + 16292973927985678*x^10 + 20712738704664489*x^11 + 15498276638623618*x^12 + 6765765599122915*x^13 + 1679542499740050*x^14 + 226176197184209*x^15 + 15278037714093*x^16 + 454493699352*x^17 + 4732512736*x^18 + 10869320*x^19 + 1575*x^20)/(1 - x)^22. - M. F. Hasler, May 02 2015
Extensions
Definition made explicit by M. F. Hasler, May 02 2015