A329708 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+2*x+...+(n+1)*x^n)^2.

1, 1, 4, 4, 1, 4, 10, 12, 9, 1, 4, 10, 20, 25, 24, 16, 1, 4, 10, 20, 35, 44, 46, 40, 25, 1, 4, 10, 20, 35, 56, 70, 76, 73, 60, 36, 1, 4, 10, 20, 35, 56, 84, 104, 115, 116, 106, 84, 49, 1, 4, 10, 20, 35, 56, 84, 120, 147, 164, 170, 164, 145, 112, 64

Offset

0,3

Links

Seiichi Manyama, Rows n = 0..99, flattened

Formula

T(n,k) = A000292(k+1) for k=0..n.

Example

Triangle begins:
1;
1, 4,  4;
1, 4, 10, 12,  9;
1, 4, 10, 20, 25, 24, 16;
1, 4, 10, 20, 35, 44, 46, 40, 25;

Prog

(PARI) for(n=0, 10, print(Vecrev(sum(k=0, n, (k+1)*x^k)^2), ", "))

Crossrefs

Cf. A000292, A002260, A084608, A329709.

Sequence in context: A213056 A135012 A156380 * A263493 A166237 A021878

Adjacent sequences: A329705 A329706 A329707 * A329709 A329710 A329711

Keyword

nonn,tabf

Author

Seiichi Manyama, Feb 29 2020

Status

approved