A349490 Sum of the n-th powers of the first n odd numbers.

1, 10, 153, 3108, 79225, 2437006, 87922513, 3642188936, 170423429841, 8891285549650, 511800291063721, 32222868466588460, 2202868653419747209, 162509566498902542934, 12868118600594014094625, 1088626666242258867384848, 97994054039441765759931169

Offset: 1

Author

Seiichi Manyama, Dec 09 2021

Keywords

• nonn

Crossrefs

Sum of the k-th powers of the first n odd numbers: A000290 (k=1), A000447 (k=2), A002593 (k=3), A002309 (k=4), A002594 (k=5), A259322 (k=6).

Cf. A005408, A031971, A061787, A103438.

Programs

Mathematica

Table[Sum[(2*k-1)^n, {k,1,n}], {n,1,20}] (* Vaclav Kotesovec, Dec 09 2021 *)

PARI

a(n) = sum(k=1, n, (2*k-1)^n);

Formula

a(n) = Sum_{k=1..n} (2*k-1)^n.

a(n) ~ 2^n * n^n / (exp(1/2) - exp(-1/2)). - Vaclav Kotesovec, Dec 09 2021