The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A309803

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A309803

a(n) is the coefficient of x^n in the polynomial Product_{i=1..n+3} (prime(i)*x-1).
(history; published version)

#12 by Robert Israel at Tue Aug 20 15:22:40 EDT 2019

STATUS

proposed

reviewed

#11 by Alois P. Heinz at Tue Aug 20 14:42:37 EDT 2019

STATUS

editing

proposed

#10 by Alois P. Heinz at Tue Aug 20 14:40:36 EDT 2019

FORMULA

a(n) = -A260613(n+3,n).

CROSSREFS

Cf. A000040, A002110, A024451, A070918, A309802, A309804, A309846, A033999, A007504, A024447, A024448, A024449, A054640, A005867, A238146, A260613.

STATUS

proposed

editing

#9 by Alexey V. Bazhin at Tue Aug 20 14:35:19 EDT 2019

STATUS

editing

proposed

#8 by Alexey V. Bazhin at Tue Aug 20 14:31:38 EDT 2019

FORMULA

a(n) = [x^n] Product_{i=1..n+3} (prime(i)*x-1).

a(n) = -abs(A070918(n+3,3)).

a(n) = -abs(A238146(n+3,n)) for n>0.

a(n) = -A260613(n+3,n)

CROSSREFS

Cf. A000040, A002110, A024451, A070918, A309802., A309804,A309846, A033999, A007504, A024447, A024448, A024449, A054640, A005867, A238146, A260613

#7 by Alois P. Heinz at Mon Aug 19 23:15:21 EDT 2019

CROSSREFS

Cf. A309802.

#6 by Alois P. Heinz at Mon Aug 19 23:14:42 EDT 2019

NAME

The fourth simplex numbers from a right-justified Phi triangle (the fourth column from a right-justified Phi triangle)

a(n) is the coefficient of x^n in the polynomial Product_{i=1..n+3} (prime(i)*x-1).

MAPLE

a:= n-> coeff(mul(ithprime(i)*x-1, i=1..n+3), x, n):

seq(a(n), n=0..20); # Alois P. Heinz, Aug 19 2019

KEYWORD

sign,easy,tabl,changed

#5 by Alois P. Heinz at Mon Aug 19 23:13:33 EDT 2019

DATA

-1, -17, -288, -5102, -107315, -2429223, -64002818, -2057205252, -69940351581, -2788890538777, -122099137635118, -5580021752377242, -276932659619923555, -15388458479166668283, -946625238259888348698, -60082571176666116692888, -4171440414742758122621945, -306149130740163500917783127, -23070829023933704057626568396, -1876269710537999457769242614062, -160042193522467556664194404154667

#4 by Alexey V. Bazhin at Sun Aug 18 10:30:39 EDT 2019

NAME

The fourth simplex numbers from a right-justified Phi triangle (the fourth column from a leftright-justified Phi triangle)

DATA

KEYWORD

nonn,sign,easy,tabl,changed

#3 by Alexey V. Bazhin at Sat Aug 17 17:00:43 EDT 2019

NAME

allocated for Alexey V. Bazhin

The fourth column from a left-justified Phi triangle

DATA

1, 17, 288, 5102, 107315, 2429223, 64002818, 2057205252, 69940351581, 2788890538777, 122099137635118, 5580021752377242, 276932659619923555, 15388458479166668283, 946625238259888348698, 60082571176666116692888, 4171440414742758122621945, 306149130740163500917783127, 23070829023933704057626568396, 1876269710537999457769242614062, 160042193522467556664194404154667

OFFSET

0,2

KEYWORD

allocated

nonn

AUTHOR

Alexey V. Bazhin, Aug 17 2019

STATUS

approved

editing