A008972 -id:A008972 - cp's OEIS frontend

A134878 Decimal expansion of Sum_{k>=1} 1/(k^2)^(k^2).

1, 0, 0, 3, 9, 0, 6, 2, 5, 2, 5, 8, 1, 1, 7, 4, 7, 9, 1, 7, 6, 7, 4, 0, 7, 2, 9, 0, 6, 1, 4, 3, 0, 6, 7, 4, 1, 0, 7, 6, 1, 2, 4, 9, 2, 4, 3, 7, 9, 2, 8, 5, 9, 4, 7, 8, 7, 6, 4, 0, 4, 7, 9, 0, 7, 9, 5, 0, 9, 9, 2, 1, 9, 0, 5, 0, 8, 6, 9, 4, 4, 5, 1, 6, 6, 8, 8, 4, 0, 2, 7, 3, 4, 8, 3, 4, 4, 6, 9, 6, 6, 8, 8, 5

Offset: 1

Artur Jasinski, Nov 14 2007

Sum_{k>=1} 1/(k^2)^(k^2) = 1.003906252581174791767407290614306741076124924379285...

Cf. A073009, A100085, A134877.

RealDigits[N[Sum[1/(n^2)^(n^2), {n, 1, 30}], 200]][[1]]

Equals Sum_{n>=1} 1/A008972(n). - R. J. Mathar, Jul 31 2025

A001330 Number of n-element algebras with 2 binary operations.

Original entry on oeis.org

1, 1, 136, 64573605, 768614338015543296, 740148683083442627372862307855625, 147760220727384062234340471228346859265417269763446784, 13097167596472133103922286145973062271265962292695709182416029922453889335720758

Offset: 0

N. J. A. Sloane

nonn

Isomorphisms classes of a set A with two functions f1,f2: A X A -> A.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737.

Cf. A001329, A001331.

a(n) = sum {1*s_1+2*s_2+...=n} (fixA[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...)) where fixA[s_1, s_2, ...] = Product_{i, j>=1} ( (sum {d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j*2)).

a(n) is asymptotic to n^(2*n^2)/n! = A008972(n)/A000142(n).

Edited and extended with formula by Christian G. Bower, Jan 06 2004

cp's OEIS Frontend

A134878 Decimal expansion of Sum_{k>=1} 1/(k^2)^(k^2).

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