A118437 Row sums of triangle A118435.

1, 2, 0, 8, -32, -128, 320, 128, 2048, 8192, -15360, 2048, -131072, -524288, 1064960, 32768, 8388608, 33554432, -66846720, 524288, -536870912, -2147483648, 4299161600, 8388608, 34359738368, 137438953472, -274810798080, 134217728

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (2, -4, 8, -64, 128, -256, 512).

Formula

G.f.: (1+8*x^3-32*x^5+384*x^6-256*x^7)/(1-2*x)/(1+4*x^2)/(1+64*x^4).

Mathematica

nmax = 27;
h[n_, k_] := Binomial[n, k]*(-1)^(Quotient[n+1, 2] - Quotient[k, 2]+n-k);
H = Table[h[n, k], {n, 0, nmax}, {k, 0, nmax}];
Cn = Table[Binomial[n, k], {n, 0, nmax}, {k, 0, nmax}];
Total /@ (H.Inverse[Cn].H ) (* Jean-François Alcover, Apr 08 2024 *)

Prog

(PARI) {a(n)=polcoeff((1+8*x^3-32*x^5+384*x^6-256*x^7)/(1-2*x)/(1+4*x^2)/(1+64*x^4+x*O(x^n)), n)}

Crossrefs

Cf. A118435 (triangle), A118436 (column 0).

Sequence in context: A076687 A062134 A002909 * A134185 A013489 A013342

Adjacent sequences: A118434 A118435 A118436 * A118438 A118439 A118440

Keyword

sign

Author

Paul D. Hanna, Apr 28 2006

Status

approved