A046825 -id:A046825 - cp's OEIS frontend

A128152 Numerator of Sum_{k=0..n} 1/binomial(n,k)^4.

1, 2, 33, 164, 20825, 10017, 25940593, 34743416, 3074035689, 672229195, 13443874324243, 431453199593, 53678600587865227, 33768054132971557, 813464644344955, 748569723383876272, 67454811525665973337193

Offset: 0

Alexander Adamchuk, May 10 2007

p^k divides a(p^k-1) for prime p and integer k > 0. p divides a(p-2) for prime p > 5.

Eric Weisstein's World of Mathematics, Binomial Sums.

Cf. A046825 (numerator of Sum_{k=0..n} 1/C(n, k)).
Cf. A100516 (numerator of Sum_{k=0..n} 1/C(n, k)^2).
Cf. A100518 (numerator of Sum_{k=0..n} 1/C(n, k)^3).

Table[ Numerator[ Sum[ 1 / Binomial[n,k]^4, {k,0,n} ] ], {n,0,50} ]

a(n) = numerator(Sum_{k=0..n} 1/binomial(n,k)^4).

A174662 Partial sums of A003149.

Original entry on oeis.org

1, 3, 8, 24, 88, 400, 2212, 14500, 110116, 951076, 9205156, 98646436, 1159016356, 14808626596, 204358994596, 3028436306596, 47955883346596, 807990334802596, 14430691329362596, 272302801683794596, 5412861968581970596

Offset: 0

Jonathan Vos Post, Nov 30 2010

Total resistance of a circuit whose n-th component is between opposite corners of an n-dimensional hypercube of unit resistors, multiplied by n!. The only prime in the sequence is 3. The subsequence of squares begins 1, 400, 9205156 = 2^2 * 37^2 * 41^2.

			a(5) = 1 + 2 + 5 + 16 + 64 + 312 = 400 = 2^4 * 5^2.

Cf. A003149, A046825, A046878, A046879, A052186, A006932, A145878.

a(n) = Sum_{i=0..n} Sum_{k=0..i} k!*(i-k)!.

Offset set to 0 by Alois P. Heinz, Jun 28 2017

A177737 Partial sums of A046878.

Original entry on oeis.org

0, 1, 2, 7, 9, 17, 30, 181, 213, 296, 369, 1802, 2449, 17790, 46001, 56448, 57664, 77009, 95190, 746935, 2289093, 3753007, 6539606, 128829523, 158059067, 298060788, 432415361, 1207300530, 1953285227, 43665199740, 124195273633

Offset: 0

Jonathan Vos Post, May 12 2010

nonn

Cf. A046878, A046825, A046879.

a(n) = Sum_{i=0..n} A046878(i).

cp's OEIS Frontend

A128152 Numerator of Sum_{k=0..n} 1/binomial(n,k)^4.

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A174662 Partial sums of A003149.

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A177737 Partial sums of A046878.

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