A316457 Expansion of x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6.

31, 512, 2943, 10624, 29375, 68256, 140287, 263168, 459999, 760000, 1199231, 1821312, 2678143, 3830624, 5349375, 7315456, 9821087, 12970368, 16879999, 21680000, 27514431, 34542112, 42937343, 52890624, 64609375, 78318656, 94261887, 112701568, 133919999

Offset: 1

Author

Colin Barker, Aug 12 2018

Keywords

• nonn
• easy

Comments

Seems to be the first column of A316349.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A316349, A316458, A316459.

Programs

PARI

Vec(x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6 + O(x^40))

PARI

a(n) = 6*n^5 + 15*n^4 + 10*n^3

Formula

G.f.: x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6.

a(n) = 6*n^5 + 15*n^4 + 10*n^3.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.