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A213575 Antidiagonal sums of the convolution array A213573. 5
1, 10, 47, 158, 441, 1098, 2539, 5590, 11909, 24818, 50967, 103662, 209521, 421786, 846947, 1697990, 3400893, 6807618, 13622095, 27252190, 54513641, 109037930, 218088027, 436189878, 872395381, 1744808338, 3489636359 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

2^n*sum( k=0..n, k^p*q^k ) for p=3, q=1/2. - Stanislav Sykora, Nov 27 2013

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..500

S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.

Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

FORMULA

a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).

G.f.: x*(1 + 4 x + x^2)/((1 - 2*x)*(1 - x)^4).

a(n) = 2^(n+1)*13-(n^3+6*n^2+18*n+26). - Stanislav Sykora, Nov 27 2013

MATHEMATICA

(See A213564.)

Table[Sum[k^3*2^(n-k), {k, 0, n}], {n, 1, 27}] (* Vaclav Kotesovec, Nov 28 2013 *)

CROSSREFS

Cf. A213564, A213500, A232603, A232604.

Sequence in context: A143895 A281767 A323799 * A319491 A034443 A304626

Adjacent sequences:  A213572 A213573 A213574 * A213576 A213577 A213578

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 18 2012

STATUS

approved

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)