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A051740 Partial sums of A007584. 5
1, 11, 45, 125, 280, 546, 966, 1590, 2475, 3685, 5291, 7371, 10010, 13300, 17340, 22236, 28101, 35055, 43225, 52745, 63756, 76406, 90850, 107250, 125775, 146601, 169911, 195895, 224750, 256680, 291896, 330616, 373065, 419475, 470085, 525141 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A000027 with A001106 (excluding 0). - Bruno Berselli, Dec 07 2012

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Murray R.Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pps. 10-20, 79-94.

LINKS

Table of n, a(n) for n=0..35.

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = C(n+3, 3)*(7n+4)/4.

a(n) = (7*n+4)*binomial(n+3, 3)/4.

G.f.: (1+6*x)/(1-x)^5.

a(n) = A080852(7,n). - R. J. Mathar, Jul 28 2016

MATHEMATICA

f[n_]:=7*n+1; s1=s2=s3=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; s3+=s2; AppendTo[lst, s3], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 25 2009 *)

PROG

(MAGMA) /* A000027 convolved with A001106 (excluding 0): */ A001106:=func<n | n*(7*n-5)/2>; [&+[(n-i+1)*A001106(i): i in [1..n]]: n in [1..36]]; // Bruno Berselli, Dec 07 2012

CROSSREFS

Cf. A001106, A007584.

Cf. A093564 ((7, 1) Pascal, column m=4).

Cf. A220212 for a list of sequences produced by the convolution of the natural numbers with the k-gonal numbers.

Sequence in context: A154106 A232613 A057813 * A263227 A144932 A072262

Adjacent sequences:  A051737 A051738 A051739 * A051741 A051742 A051743

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, Dec 07 1999

STATUS

approved

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Last modified October 19 02:23 EDT 2018. Contains 316327 sequences. (Running on oeis4.)