A126713 -id:A126713 - cp's OEIS frontend

A038200 Row sums of triangle K(m, n), inverse to triangle T(m,n) in A020921.

1, 0, -1, 3, -8, 21, -54, 134, -318, 720, -1560, 3259, -6641, 13391, -27107, 55657, -116244, 245823, -521738, 1101566, -2299215, 4730990, -9601095, 19273729, -38446742, 76598275, -153119606, 308061214, -624460449, 1274268038, -2611866713, 5362888620, -11003127203, 22516189988

Offset: 1

Temba Shonhiwa (Temba(AT)maths.uz.ac.zw)

sign

The triangle K is A126713.

Temba Shonhiwa, A Generalization of the Euler and Jordan Totient Functions, Fib. Quart., 37 (1999), 67-76.
N. J. A. Sloane, Transforms

Cf. A126713, A020921.

Inverse binomial transform of tau(n) = A000005(n): Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*A000005(k). - Vladeta Jovovic, Oct 29 2002

E.g.f.: exp(-x)*Sum_{k>=1} d(k)*x^k/k!. - Ilya Gutkovskiy, Nov 26 2017

Better description from Michael Somos

A039912 Triangle related to number of compositions of n into relatively prime summands.

Original entry on oeis.org

1, 1, -2, 1, -3, 4, 1, -4, 6, -8, 1, -5, 10, -9, 16, 1, -6, 15, -20, 9, -32, 1, -7, 21, -35, 36, 0, 64, 1, -8, 28, -56, 70, -64, -27, -128, 1, -9, 36, -84, 126, -125, 120, 81, 256, 1, -10, 45, -120, 210, -252, 200, -240, -162, -512, 1, -11, 55, -165, 330, -462, 463, -275, 496, 243, 1024, 1, -12, 66, -220, 495, -792, 924

Offset: 2

N. J. A. Sloane

			Triangle begins:
  1;
  1, -2;
  1, -3,  4;
  1, -4,  6,  -8;
  1, -5, 10,  -9, 16;
  1, -6, 15, -20,  9, -32;
  1, -7, 21, -35, 36,   0, 64;
  ...

H. W. Gould, Binomial coefficients, the bracket function and compositions with relatively prime summands, Fib. Quart. 2 (1964), 2.

Cf. A126713.

More terms from Vladeta Jovovic, Feb 26 2008

cp's OEIS Frontend

A038200 Row sums of triangle K(m, n), inverse to triangle T(m,n) in A020921.

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