A118583 Numerator of sum of first p reciprocals of p-simplex numbers divided by p^4, where p = prime(n) for n > 2.

1, 5, 53, 789, 237493, 2576561, 338350897, 616410400171, 2603853251291, 5745400286707685, 3081677433937346539, 41741941495866750557, 7829195555633964779233, 21066131970056662377432067

Offset: 3

Author

Alexander Adamchuk, May 09 2007

Keywords

• nonn

Examples

			Prime(3) = 5.
a(3) = 1 because A118431(5)/5^4 = 1, where A118431(5) = Numerator[ 1/C(4+1,5) + 1/C(4+2,5) + 1/C(4+3,5) + 1/C(4+4,5) +1/C(4+5,5) ] = Numerator[ 1/1 + 1/6 + 1/21 + 1/56 + 1/126 ] = 625.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 3..250
• Eric Weisstein's World of Mathematics, Composition.
• Eric Weisstein's World of Mathematics, Tetrahedral Number.
• Eric Weisstein's World of Mathematics, Triangular Number.

Crossrefs

Cf. A022998 = Numerator of sum of reciprocals of first n triangular numbers

Cf. A118391 = Numerator of sum of reciprocals of first n tetrahedral numbers A000292.

Cf. A118431 = Numerator of sum of reciprocals of first n 5-simplex numbers A000389.

Programs

Mathematica

Table[Numerator[Sum[1 /Binomial[ n+Prime[k]-1, Prime[k]], {n,1,Prime[k]} ]]/ Prime[k]^4, {k,3,25}]

PARI

for(n=3,10, print1(numerator(sum(k=1,prime(n), 1/(binomial(k+ prime(n)-1, prime(n)))))/prime(n)^4, ", ")) \\ G. C. Greubel, Nov 25 2017

Formula

a(n) = numerator( Sum_{k=1..prime(n)} ( 1/binomial( k + prime(n) - 1, prime(n) ) ))/prime(n)^4 for n > 2.