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A027220 a(n) = Sum_{k=0..n} (k+1) * A026736(n,n-k). 1
1, 3, 8, 20, 52, 121, 301, 675, 1628, 3570, 8426, 18202, 42288, 90374, 207464, 439800, 1000194, 2106961, 4755715, 9967599, 22359788, 46670273, 104154703, 216643945, 481381746, 998346275, 2210037191, 4571884119, 10088030640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

MATHEMATICA

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]]; Table[Sum[(k+1)*T[n, n-k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Jul 19 2019 *)

PROG

(Sage)

@CachedFunction

def T(n, k):

    if (k==0 or k==n): return 1

    elif (mod(n, 2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1)

+ T(n-1, k)

    else: return T(n-1, k-1) + T(n-1, k)

[sum((k+1)*T(n, n-k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jul 19 2019

CROSSREFS

Cf. A026736.

Sequence in context: A077997 A294407 A295346 * A305823 A333679 A230953

Adjacent sequences:  A027217 A027218 A027219 * A027221 A027222 A027223

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 29 08:45 EDT 2020. Contains 337428 sequences. (Running on oeis4.)